1. An object in motion tends to stay in
motion because it has ___?____. (inertia or
terminal velocity)

Answers

Answer 1

Answer: intertia

Explanation:


Related Questions

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm (red) and 486 nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 520 lines/mm , and the light is observed on a screen 1.4 m behind the grating.

Required:
What is the distance between the first-order red and blue fringes?

Answers

Answer:

0.143 m

Explanation:

Since

d = 1/N = 1/520 = 1.92 * 10^-3 mm

For red light;

θ = sin^-1  (1 * λred/d) =  sin^-1  (1 * 656 * 10^-9/1.92 * 10^-6) = 19.98°

L = 1.4 * (tan 19.98) = 0.509 m

For blue light;

θ = sin^-1  (1 * λblue/d) =  sin^-1  (1 * 486 * 10^-9/1.92 * 10^-6) = 14.66°

L = 1.4 * (tan 14.66°) = 0.366 m

Distance between the first-order red and blue fringes= 0.509 m - 0.366 m = 0.143 m

A plot of land contains 3.6 acres. How many square meters does it contain? [1 acre = 43,560 ft?)

Answers

Answer:

It contains approximately 14,568.7 square meters

Explanation:

Area Units Conversion

There are several units to express the area of a shape:

\(cm^2,\ m^2,\ km^2,\ ft^2,\ in^2,\ acres, \ hectares\)

The process of expressing the area from one unit to the other is called a conversion.

Specifically, we are interested in converting from acres to square meters. The rule to make the conversion is:

\(1 acre = 4,046.86\ m^2\)

The plot of land has 3.6 acres, thus its area is:

\(3.6 * 4046.86 =14,568.696\ m^2\)

It contains approximately 14,568.7 square meters

how does mass and speed affects kinetic energy

Answers

The kinetic energy affects when there is an increase in the mass and speed of the object.

When the object is in motion, Kinetic energy is observed. Kinetic energy is the product of the mass and square of the speed of an object. It depends on both the mass and speed of the object.

K.E = 1/2 (mv²), where m is the mass of the object and v is the speed of the object. Thus, the kinetic energy is directly proportional to the mass and speed of the object.

When speed increases two times, the kinetic energy increases by four times. When speed increases 3 times, the kinetic energy increases by 9. If the object has more mass, the kinetic energy also increases, and vice-versa.

Hence, the kinetic energy increases with the increase in mass and speed of the object.

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Approximately how many times louder is a 150-dB sound than a 80-dB sound?

Answers

a 150-dB sound is approximately 10 million times louder than an 80-dB sound.

What is the range of sound?

Provide instances of the differences between the audible, ultrasonic, and infrasonic frequency ranges. Three sorts of sound waves, each covering a distinct frequency range, are used. These are what they are:

Waves that fall inside the ear's sensitivity range are referred to be audible waves.Infrasonic waves are those whose frequencies fall below the range of human hearing. Ultrasonic waves are those with frequencies higher than those of sound.

The difference in decibels between two sounds is related to the ratio of their intensities (or power) by the following formula:

dB₂ - dB₁ = 10 log10(I₂ / I₁)

where dB₁ and dB₂ are the decibel levels of the two sounds, and I₁ and I₂ are their intensities (or power).

Using this formula, we can find the ratio of the intensity of a 150-dB sound to that of an 80-dB sound:

150 dB - 80 dB = 10 log10(I₁₅₀ / I₈₀)

70 = 10 log10(I₁₅₀ / I₈₀)

7 = log10(I₁₅₀ / I₈₀)

10^7 = I₁₅₀ / I₈₀

I₁₅₀  = 10^7 * I₈₀

This shows that the intensity of a 150-dB sound is 10 million times greater than that of an 80-dB sound.

Therefore, a 150-dB sound is approximately 10 million times louder than an 80-dB sound.

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A 66 kg driver gets into an empty taptap to start the day's work. The springs compress 2.3×10−2 m
. What is the effective spring constant of the spring system in the taptap?
Enter the spring constant numerically in newtons per meter using two significant figures

Answers

Explanation:

You want  N/m

 N = 66 * 9.81

 m = 2.3 x 10^-2 m

66* 9.81 / 2.3 x 10^-2  = 28150 =  28 000 N/m    to two S D

Condyloid joints are, logically enough, created by joints at condyle bone markings.
True or False

Answers

Answer: False

Explanation:

It's received in elliptical cavities.

False. The statement is not entirely accurate. Condyloid joints are a type of synovial joint that allow movement in two planes, similar to an ellipsoid joint.

These joints are characterized by an oval-shaped projection of one bone fitting into an elliptical cavity of another bone. The term "condyle" does refer to a rounded projection or bump on a bone, but not all condyle bone markings create condyloid joints.

Condyloid joints are found in various parts of the body, such as the wrist (between the radius and carpal bones) and the knuckles (between the metacarpal bones and phalanges). They allow for movements such as flexion, extension, abduction, adduction, and circumduction.

It's important to note that the formation of a condyloid joint involves not only the presence of condyle bone markings but also the specific structural arrangement of the bones and the presence of articular cartilage, joint capsule, and synovial fluid. Therefore, while the term "condyle" is related to these joints, it does not accurately capture the complexity of their formation and function.

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The monster wants to make himself known to the family in the cottage in chapters 9-12 of Frankenstein. He decides he can't do that until he masters something. What skill
must he master?
A. How to dress properly
B. Language
C. The rules of etiquette
D. Music

Answers

Answer:

c

Explanation:

how can you Make different objects using blocks

Answers

You can stack the blocks together to make different objects you can also lay them out and make it into a different object

Weight is best defined as _____. A the amount of space an object takes up B the speed of an object C the force of gravity on an object D the amount of energy in an object

Answers

Weight is best defined as C) the force of gravity on an object.

When a skater pulls her arms in, it
reduces her moment of inertia from
2.12 kg m² to 0.699 kg-m². If she was
initially spinning 3.25 rad/s, what is
her final angular velocity?

Answers

The skater's final angular velocity is approximately 9.86 rad/s.

The skater's final angular velocity can be calculated using the principle of conservation of angular momentum. The equation for angular momentum is given by:

L = Iω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Initially, the skater has an angular momentum of:

L_initial = I_initial * ω_initial

Substituting the given values:

L_initial = 2.12 kg m² * 3.25 rad/s

The skater's final angular momentum remains the same, as angular momentum is conserved:

L_final = L_initial

The final moment of inertia is given as 0.699 kg m². Therefore, the final angular velocity can be calculated as:

L_final = I_final * ω_final

0.699 kg m² * ω_final = 2.12 kg m² * 3.25 rad/s

Solving for ω_final:

ω_final = (2.12 kg m² * 3.25 rad/s) / 0.699 kg m²

Hence, the skater's final angular velocity is approximately 9.86 rad/s.

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a vector has a magnitude of 34 meters and an angle of 26 degrees what is the y-component of the vector? (i'd appreciate if anyone could answer this)​

Answers

The y-component of the vector is approximately 14.67 meters.

To find the y-component of the vector, we need to use trigonometry. Given that the vector has a magnitude of 34 meters and an angle of 26 degrees, we can break down the vector into its x and y components.

Step 1: Identify the known values:

Magnitude of the vector (r) = 34 meters

Angle (θ) = 26 degrees

Step 2: Determine the y-component using trigonometry:

The y-component can be found using the formula:

y = r * sin(θ)

Step 3: Calculate the y-component:

Substituting the known values into the formula:

y = 34 * sin(26 degrees)

y ≈ 14.67 meters

Therefore, the y-component of the vector is approximately 14.67 meters.

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What advantage is there in measuring your distance from I1 to I1' and dividing by 2 rather than measuring the distance OI1 directly

Answers

Measuring the distance from  \(I_1 \ to \ I_1'\) and dividing by 2 has advantage of achieving a more accurate result compared to measurement taking directly.

Measuring the distance from \(I_1 \ to \ I_1'\) is equivalent to the double of the distance.

This method of measurement gives a more accurate result because it minimizes error that may result from taking readings form the intervals. It ensures more accurate result compared to the measurement obtained when \(OI_1\) is measured directly.

\(OI_1 = \frac{I_1 + I_1'}{2}\)

Thus, we can conclude that measuring the distance from  \(I_1 \ to \ I_1'\) and dividing by 2 has advantage of achieving a more accurate result compared to measurement taking directly.

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Which of the following statements is true?

Which of the following statements is true?

Answers

Answer:

Aluminum and steel are good conductors of electricity.

Explanation:

1) All materials are good conductors of electricity.

This is false because nonmetal materials such as plastic or wood cannot conduct electricity.

2) Aluminum and steel are good conductors of electricity.

This is true. All metals are conductors of electricity.

3) Gold and wood are poor conductors of electricity.

This is false. Although gold can conduct electricity, wood can't.

4) Plastic and copper are good conductors of electricity.

This is false. Although copper can conduct electricity, plastic can't.

I hope this helps!

Answer:

B) Aluminum and steel are good conductors

Explanation:

Why do bodies of water tend to moderate temperature swings from day to day?
A: bodies of water reduce insolation
B: The presence of water disrupts the Milankovitch cycle
C: Bodies of water deflect prevailing winds
D: Water has a high heat capacity
pls help​

Answers

Answer: D: Water has a high heat capacity.

Explanation:

Bodies of water tend to moderate temperature swings from day to day primarily because water has a high heat capacity. Heat capacity refers to the amount of heat energy required to raise the temperature of a substance. Water has a relatively high heat capacity compared to land, meaning it can absorb and store a significant amount of heat energy without experiencing large temperature changes.

During the day, when the sun is shining, bodies of water absorb heat energy from the sunlight. As water has a high heat capacity, it can absorb a considerable amount of heat without experiencing a significant rise in temperature. This absorption of heat helps to keep the surrounding areas relatively cooler, moderating the temperature.

During the night, when the air temperature drops, bodies of water release the stored heat energy back into the atmosphere, which can help to warm up the surrounding areas. This release of heat helps to prevent rapid cooling and keeps the temperature relatively stable.

In contrast, land surfaces have a lower heat capacity, so they heat up and cool down more quickly compared to bodies of water. This is why areas located near bodies of water tend to experience milder and more stable temperatures, with less extreme temperature swings from day to day.

Therefore, the high heat capacity of water is the primary reason why bodies of water tend to moderate temperature swings from day to day.

When discussing you will be defending your thoughts of the following questions:

1. Children’s appetites and willingness to eat are strongly influenced by the mealtime environment. Identify and briefly discuss several features that can be used to create an atmosphere that encourages children to eat.
2. Review the My Plate food guide and suggest appropriate snack foods from each food group that would be appropriate for school-age children.
3. In what ways can adults help children learn to enjoy nutritious food and establish healthy eating habits?

Answers

To encourage children to eat, create a pleasant and distraction-free mealtime environment, serve a variety of visually appealing and small portions of favorite foods, involve them in meal planning and preparation, provide a relaxed and comfortable atmosphere, and avoid using food as a reward or punishment. Appropriate snack foods from each food group for school-age children can be selected from fruits, vegetables, grains, protein, and dairy. Adults can help children learn to enjoy nutritious food and establish healthy eating habits by modeling healthy eating behaviors, involving children in grocery shopping and meal planning, making meals enjoyable and fun, providing healthy food choices, and avoiding using food as a reward or punishment.

1. To create an atmosphere that encourages children to eat, several features can be used, such as:

A pleasant and inviting mealtime environment that is free of distractions such as television, mobile phones, or tablets.

Serve a variety of colorful, visually appealing foods in small portions, making sure to include favorite foods of the child.

Involve children in meal planning and preparation, giving them the opportunity to select foods and participate in simple meal preparation tasks.

Provide a relaxed and comfortable atmosphere by allowing enough time for meals and offering positive reinforcement for good eating behaviors.

Avoid using food as a reward or punishment and ensure that mealtimes are stress-free and enjoyable for children.

2. MyPlate is a visual representation of the five food groups that form a healthy and balanced diet. Appropriate snack foods from each food group for school-age children could include:

Fruits: apple slices, berries, bananas, or orange wedges.

Vegetables: carrot sticks, cherry tomatoes, cucumber slices, or celery sticks.

Grains: whole-grain crackers, granola bars, rice cakes, or air-popped popcorn.

Protein: hard-boiled eggs, cheese sticks, nut butter, or hummus.

Dairy: yogurt, milk, or cheese cubes.

3. Adults can help children learn to enjoy nutritious food and establish healthy eating habits by:

Modeling healthy eating behaviors and food choices themselves.

Encouraging children to try new foods and flavors, involving them in grocery shopping, and meal planning.

Making meals enjoyable and fun by creating a positive mealtime environment and involving children in meal preparation tasks.

Providing healthy food choices and limiting the availability of unhealthy options at home and school.

Offering regular mealtimes and avoiding using food as a reward or punishment.

Hence, Encourage children to eat by providing a pleasant and distraction-free mealtime environment, serving a variety of visually appealing and small portions of favorite foods, involving them in meal planning and preparation, providing a relaxed and comfortable environment, and avoiding using food as a reward or punishment. Fruits, vegetables, grains, protein, and dairy are examples of appropriate snack foods from each food group for school-age children. Adults can assist children in learning to enjoy nutritious food and develop healthy eating habits by modeling healthy eating behaviors, involving children in grocery shopping and meal planning, making meals enjoyable and fun, providing healthy food options, and avoiding using food as a reward or punishment.

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A teacher gives students a sunglasses lens and asks them to observe the surface of a pond on a sunny day. The students notice that the water on the surface of the pond appears brighter and then dimmer when they rotate the lens as they look through it at the pond. The teacher asks the students to explain this observation. Which of the following student statements provides a correct explanation?
A. The lenses of the sunglasses absorb and transmit light of different wavelengths or offerent angles of lens rotation, thus transmitting more or less light to our eyes
B. Rotating the sunglasses changes the index of retraction of the lenses, co more light is tetracted away from our eyes at some angles
C. Only some of the light is reflected from the surface of the pond and rotating the lens causes more or less light to be transmitted at some angles
D. The light is linearly polarized when it is reflected off the surface of the pond, and the lens is a polariangles that transmits more light at certain angles

Answers

Answer:

Option D

Explanation:

Option (A) is incorrect because transmission of few wavelength will procure visibility of only few colours and not all. Option B is also incorrect as refraction index remains same as it does not changes with the change in angle. Option C is also incorrect because changing orientation of only some of the light with not make any significant difference

Option D is correct because sunlight is a unpolarised light  which can be polarised using reflection. Now when sunlight gets  partially linearly polarized after reflection from the lake, it can be viewed by the observer's eye through the lens.

B is the statements provide is a correct explanation. Rotating the sunglasses changes the index of refraction of the lenses, so more light is retracted away from our eyes at some angles.

What is a refractive index?

The refractive index n is defined as the ratio of the sine of the incidence angle to the sine of the refraction angle, i.e., n = sin I / sin r.

The velocity of light c of a given wavelength in empty space divided by its velocity v in a substance, or n = c/v, is also equal to the refractive index.

Rotating the sunglasses changes the index of refraction of the lenses, so more light is retracted away from our eyes at some angles.

Hence option B is correct.

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A 1.2-kg mass is projected from ground level with a velocity of 31.3 m/s at some unknown angle above the horizontal. A short time after being projected, the mass barely clears a 16-m tall fence. Disregard air resistance and assume the ground is level. What is the kinetic energy of the mass as it clears the fence

Answers

Answer:

The kinetic energy will be "399.65 J".

Explanation:

Given:

Mass,

m = 1.2 kg

Velocity,

v = 31.3 m/s

The total energy of mass will be:

⇒ \(E=K+U\)

or,

⇒ \(E=.5mv^2+mgh\)

By putting the values, we get

        \(=.5(1.2)(31.3)^2+0\)

        \(=0.6\times 979.69+0\)

        \(=587.81 \ J\)

Since,

The system's total energy is unchanged, then

⇒ \(E=K+U\)

or,

⇒ \(E=K+mgh\)

   \(587.81=K+1.2(9.8)(16)\)

   \(587.81=K+188.16\)

          \(K=587.81-188.16\)                

               \(=399.65 \ J\)

As rotational speed increases, thrust____?

increases exponentially.

increases at the same rate.

decreases exponentially.

decreases at the same rate

Answers

Increases exponentially is your correct answer

A 35.30-kg box is attached to a light string that is wrapped around a cylindrical frictionless spool of radius 10.0 cm and moment of inertia 4.00 kg * m^2. The spool is suspended from the ceiling, and the box is then released from rest a distance from rest a distance 3.50 m above the floor. How long does it take for the box to reach the floor?

Answers

Answer:

The velocity of the box is related to the angular velocity of the spool, which is given by the equation:

v = r * ω

where r is the radius of the spool and ω is the angular velocity of the spool. The angular velocity of the spool, in turn, is related to the torque applied to the spool by the tension in the string, which is given by the equation:

τ = I * α

where τ is the torque, I is the moment of inertia of the spool, and α is the angular acceleration of the spool.

The tension in the string is equal to the weight of the box, which is given by:

T = m * g

Putting all of these equations together, we can solve for the time it takes for the box to reach the floor. Here's how:

First, we can find the angular acceleration of the spool using the torque equation:

τ = I * α

T = m * g = τ

m * g = I * α

α = (m * g) / I

α = (35.30 kg * 9.81 m/s^2) / 4.00 kg*m^2

α = 86.53 rad/s^2

Next, we can find the angular velocity of the spool using the kinematic equation:

ω^2 = ω_0^2 + 2 * α * θ

where ω_0 is the initial angular velocity (which is zero), θ is the angle through which the spool has turned (which is equal to the distance the box has fallen divided by the radius of the spool), and ω is the final angular velocity (which is what we want to find). Solving for ω, we get:

ω^2 = 2 * α * θ

ω = sqrt(2 * α * θ)

ω = sqrt(2 * 86.53 rad/s^2 * (3.50 m / 0.10 m))

ω = 166.6 rad/s

Finally, we can find the time it takes for the box to reach the floor using the equation:

v = r * ω

v = 0.10 m * 166.6 rad/s

v = 16.66 m/s

t = d / v

t = 3.50 m / 16.66 m/s

t = 0.21 s

An astronaut brings a cube from the Earth to the Moon.
What is true about the inertial mass and weight of the cube?
Note that the gravitational acceleration on the Moon is about 1.6m/s^2

A) The inertial mass increases but the weight decreases.
B) Both the inertial mass and weight decrease.
C) The inertial mass decreases but the weight increases.
D) The inertial mass remains constant but the weight decreases.

Answers

Answer:

Answer D. Inertial mass constant, weight decreases.

Explanation:

Khan Academy

An astronaut brings a cube from the Earth to the Moon.What is true about the inertial mass and weight

a spring is stretched by 35 cmcm and attached to a 500 gg air-track glider, which is then released. the spring does 0.20 jj of work on the glider as it returns to its equilibrium length.What is the value of the spring constant?

Answers

The value of the spring constant for the spring stretched by 35 cmcm  is  0.005714 J/cm.

To calculate the spring constant, the equation Work = Force x Distance is used. The work of the spring (0.20 J) is known, as well as the distance the spring is stretched (35 cm). Therefore, the force is calculated by dividing the work by the distance. The force is then divided by the distance the spring is stretched back to its equilibrium position (35 cm) to find the spring constant. The spring constant is the amount of force required to stretch the spring 1 cm. In this example, the spring constant is 0.005714 J/cm.

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Water flows at a speed of 13 m/s through a pipe that has a diameter of 1.2 m. What is the
diameter of the smaller end of the pipe that the water comes out with a speed of 30 m/s?

Answers

The diameter of the smaller end of the pipe is approximately 0.78 meters.

To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.

The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity

Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2

Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2

Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30

Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30

0.36 * 13 = (diameter2/2)^2 * 30

4.68 = (diameter2/2)^2 * 30

Dividing both sides by 30:
0.156 = (diameter2/2)^2

Taking the square root of both sides:
0.39 = diameter2/2

Multiplying both sides by 2:
0.78 = diameter2

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What is SeaWorld?
What is this
What is that

Answers

SeaWorld is a chain of theme parks and oceanariums that showcase marine life through educational exhibits, live shows, and thrilling rides. While it has faced criticism for its treatment of animals, SeaWorld has made changes to prioritize conservation and phased out its orca breeding program.

SeaWorld is a chain of theme parks and oceanariums that primarily focuses on marine life and entertainment. The company operates various parks across the United States, including SeaWorld parks in Orlando, San Diego, and San Antonio, as well as Busch Gardens parks in Tampa and Williamsburg. SeaWorld offers a combination of educational exhibits, live shows, and thrilling rides, with a special emphasis on marine animals such as dolphins, whales, sea lions, penguins, and sharks.

SeaWorld parks provide visitors with opportunities to observe and interact with marine creatures up close, while also offering educational programs that aim to raise awareness about marine conservation and preservation. The parks feature captivating shows featuring trained animals, where they perform impressive behaviors and stunts, showcasing their intelligence and natural abilities.

Over the years, SeaWorld has faced criticism from animal rights activists and environmentalists, who argue that the captivity and use of marine animals for entertainment purposes is unethical and harmful to the animals' well-being. These concerns have led to significant changes in the company's practices, including the phasing out of its orca breeding program and the introduction of more educational and conservation-focused initiatives.

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Charges may be transferred by:

A) induction
B) insulation
C) reduction
D) conduction

Answers

A) induction and D) conduction

Answer:

D) conduction

Explanation:

A falling object with a mass of 2.55 kg encounters 4.0 N of air resistance. What is the acceleration of the object? (Choose up to be the positive direction, and remember the definition of weight).

Answers

The acceleration of the falling object with a mass of 2.55 kg that encounters 4.0 N of air resistance is 1.57m/s².

How to calculate acceleration?

Acceleration is change of velocity with respect to time (can include deceleration or changing direction).

The acceleration of a body can be calculated by using the following expression;

a = F/m

Where;

a = acceleration (m/s²)F = force (N)m = mass (kg)

According to this question, a mass of 2.55 kg encounters 4.0 N of air resistance. The acceleration of the object can be calculated as follows:

a = 4N ÷ 2.55kg

a = 1.57m/s²

Therefore, 1.57m/s² is the acceleration of the object.

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PLEASE HELP!!!!! ILL GIVE BRAINIEST IF ANSWER IS CORRECT!!!!
An electron is pushed eastwards with a force of 1.64 x 10-21 N when placed in an electric
field. Determine the
(a) magnitude and
(b) direction of the electric field.

Answers

Answer: 1.02 x 10^-2 N/C to the east

Explanation:

Hi,

To find the magnitude of the electric field in this problem, you simply have to use the formula F = qE

F = Force

q = charge of the particle

E = magnitude of the electric field

Here, we are told that a force is being acted on an electron and we aren't told any specific quantity of charge for the electron. Therefore, we can assume that the charge of the electron will be its conventional charge of 1.602 x 10^-19 C

We are also given the force which is 1.64 x 10^-21 N

We solve for E

E = F/q

We plug in

E = (1.64 x 10^-21 N)/(1.602 x 10^-19 C)

E = 1.02 x 10^-2 N/C

The direction will be the east because the angle didn't change.

As part of a movie stunt, a full-size remote-controlled car is driven horizontally off a 9.00 m tall cliff at 24.40 m/s. How far (Δx) from the bottom of the cliff does the car land?

Answers

Explanation:

Find the time it takes to hit the  bottom....then multiply this time by the horizontal velocity .......

Time to hit bottom :

       d = 1/2 at^2

        9 m  = 1/2 (9.81 m/s^2) (t^2)    shows  t = 1.35 s

Now the horizontal displacement is

      x = rate * time = 24.40 m/s * 1.35 s = 33.1 m

The number of distinct ways of placing four indistinguishable balls into five distinguishable boxes is _____

Answers

The number of distinct ways of placing four indistinguishable balls into five distinguishable boxes is 20.

To solve this problem, we can use the stars and bars method, which is a combinatorial technique used to count the number of ways to distribute indistinguishable objects into distinguishable containers. In this case, we have four indistinguishable balls and five distinguishable boxes.

The stars and bars method works by representing each ball as a star and using bars to separate the balls into different boxes. For example, if we wanted to distribute two balls into three boxes, we could use the following diagram:

* | * * | *

In this diagram, the first and last bars represent the boundaries of the containers, while the stars represent the balls.

The second bar separates the first two balls from the last ball, indicating that the first two balls are in the first container and the last ball is in the third container.

To distribute four balls into five boxes, we need to use three bars to separate the balls into four groups. We have a total of six spaces to place the bars (including the boundaries), and we need to choose three of them to place the bars.

Therefore, the number of distinct ways to place four indistinguishable balls into five distinguishable boxes is the same as the number of ways to choose three spaces out of six, which is:

6 choose 3 = (6!)/(3!3!) = 20

Therefore, there are 20 distinct ways to place four indistinguishable balls into five distinguishable boxes using the stars and bars method.

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Which activities demonstrate reaction time the most?

Which activities demonstrate reaction time the most?

Answers

Answer:

A goal keepee catering the ball in time is answer

Betty, with a mass of 46.8 kilograms, sits on a playground swing that hangs 0.417 meters above the ground. Brian pulls the swing back and releases it when the seat is 1.22 meters above the ground. If 179 joules of energy is converted to thermal energy, how fast does Betty move through the lowest position? Include units in your answer. Answer must be in 3 significant digits.

Answers

In order to determine the sped of Betty at the lowest position, proceed as follow:

The potential energy for a height of 1.22m is:

\(\begin{gathered} U_1=m\cdot g\cdot h_1 \\ U_1=(46.8kg)(9.8\frac{m}{s^2})(1.22m) \\ U_1\approx559.54J \end{gathered}\)

The potential energy at the lowest point is:

\(\begin{gathered} U_2=m\cdot g\cdot h_2 \\ U_2=(46.8kg)(9.8\frac{m}{s^2})(0.417m) \\ U_2\approx191.25J \end{gathered}\)

Consider that at the starting point all the mechanical energy is potential energy (559.54J). Moreover, when Betty moves through the lowest point, part of the mechanical energy becomes thermal energy and kinetic energy.

Take into account that the for the lowest point, the sum of thermal energy, kinetic energy and potential energy must be equal to the total mechanical energy:

U2 + K + Th = 559.54J

where K is the kinetic energy and Th is the thermal energy. Consider that

Th = 179J

U2 = 191.25J

Solve the equation for K and replace the values of the other contributions to the total energy:

K = 559.54J - U2 - Th

K = 559.54J - 191.25J - 179J

K = 189.29J

Next, take into account that the kinetic energy is given by:

\(K=\frac{1}{2}mv^2\)

solve the previous equation for v and replace the values of K and m:

\(\begin{gathered} v=\sqrt[\square]{\frac{2K}{m}} \\ v=\sqrt[]{\frac{2(189.29J)}{46.8\operatorname{kg}}} \\ v\approx2.84\frac{m}{s} \end{gathered}\)

Hence, Betty moves with a speed of approximately 2.84m/s through the lowest point.

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