When it comes to fitness, at the end of the day the most important thing is

The potential energy of the roller coaster is 176,400 J (joules).

The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.

In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).

Using the formula, we can calculate the potential energy:

PE = mgh

= (900 kg)(9.8 \(m/s^2\))(20 m)

= 176,400 J

Therefore, the potential energy of the roller coaster is 176,400 J (joules).

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Answer:

Its nymber 2

Explanation:

The ball's height at time t is

y = (20.0 m/s) t - 1/2 g t²

where g is the acceleration due to gravity, with magnitude 9.80 m/s².

Also, recall that

v² - u² = 2 a ∆y

where u is the initial velocity, v is the final velocity, a is the acceleration, and ∆y is the change in height. Let Y be the maximum height. At this height, v = 0, so

- (20.0 m/s)² = 2 (-g) Y

==>  Y ≈ 20.408 m

Plug this into the first equation and solve for t :

Y = (20.0 m/s) t - 1/2 (9.80 m/s²) t²

==>  t ≈ 2.04 s

The ball's velocity at time t is

v = 20.0 m/s - g t

After t = 3.0 s, its velocity will be

v = 20.0 m/s - (9.80 m/s²) (3.0 s)

v = -9.40 m/s

or 9.40 m/s in the downward direction.

After the elastic collision, velocity of the 8 kg mass is calculated as 13.525 m/s.

A collision in which there is no net loss in kinetic energy in the system as a result of the collision is called  an elastic collision. Momentum and kinetic energy are conserved quantities in elastic collisions.

m1v1i + m2v2i = m1v1f +m2v2f

m1 =3 kg  ; v1i = 14.2 m/s

m2 = 8kg ; v2i= 8.2 m/s

v1f= 0

v2f = m1v1i + m2v2i / m2

= (3* 14.2) + (8 * 8.2)/8

V2f = 13.525 m/s

Velocity of the 8 kg mass is 13.525 m/s.

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The identification requires a record of the prints of all 10 fingers of a person made using ink or digital imaging is Fingerprint identification.

The print of fingers are taken by the digital imaging to recognize a specific person, specially used to detect criminals.

Therefore, Fingerprint identification requires a record of the prints of all 10 fingers of a person made using ink or digital imaging.

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The polynomial relationship between position and time for the bowling ball is linear.

A linear relationship between two variables is a term used to describe a straight-line relationship between the two variables.

Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.

From the equation of linear relationship between two variable, the highest power of x is one.

The given equation for position and time;

x(t) = vot + xo

From this given equation, the highest power of t is one, hence it is called linear relationship.

Thus, the polynomial relationship between position and time for the bowling ball is linear.

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Answer:

Explanation:

angle θ = 110 arcsec

= 110 /60 arcmin

= 1.8333 arcmin

= 1.8333 / 60 degree

= .030555 degree

= .030555 x π / 180 radian

= 5.33 x 10⁻⁴ radian .

linear diameter = angular diameter in radian x distance

= 5.33 x 10⁻⁴ x 25000

= 13.325 m

linear diameter of object = 13.325 m .

The hiker made it to a safe landing on the other side of the gap after travelling horizontally at 2.49 m.

The time taken for the hiker to fall from the given height is calculated as follows;

h = vt + ¹/₂gt²

where;

h = ¹/₂gt²

t = √(2h/g)

t = √[(2 x 0.6) / (9.8)]

t = 0.35 seconds

The horizontal velocity of the hiker during the period of acceleration is calculated as follows;

Vₓ = at

Vₓ = (5.92 m/s²) x (1.2 s)

Vₓ = 7.104 m/s

The horizontal distance travelled during the time period of 0.35 seconds;

X = Vₓt

X = 7.104 x 0.35

X = 2.49 m

Thus, the hiker made it to a safe landing on the other side of the gap which is 2.3 m wide and smaller to his horizontal displacement of 2.49 m.

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Answer:

Explanation:

The solar-powered reverse-osmosis (RO) water plant would likely fall under the category of "durable goods" or "capital goods."

Durable goods, also known as consumer durables, are goods that are expected to last for a period of three years or more. Capital goods, on the other hand, are goods used in the production of other goods and services and are expected to last for several years.

The characteristics of durable goods include:

Long-lasting and expected to last several years

High initial cost

Typically used for personal or household consumption

Often purchased infrequently

Can appreciate in value over time

The characteristics of capital goods include:

Long-lasting and expected to last several years

High initial cost

Used in the production of other goods and services

Often purchased by businesses or industries

Depreciate in value over time as they are used up in the production process.

Given that the solar-powered RO water plant is expected to last for several years, is used in the production of water for personal or household consumption, and has a high initial cost, it is likely to fall under the category of durable goods.

Since the decay rate is dependent upon the number of radioactive atoms, in terms of chemical kinetics, one can say that radioactive decay is a first order reaction process.

What is radioactivity ?

Radioactive decay is the loss of elementary particles from an unstable nucleus, ultimately changing the unstable element into another more stable element. There are five types of radioactive decay: alpha emission, beta emission, positron emission, electron capture, and gamma emission. Each type of decay emits a specific particle which changes the type of product produced. The number of protons and neutrons found in the daughter nuclei (the nuclei produced from the decay) are determined by the type of decay or emission that the original element goes through.

Also, radioactive decay is an exponential decay function which means the larger the quantity of atoms, the more rapidly the element will decay. Mathematically speaking, the relationship between quantity and time for radioactive decay can be expressed in following way:

dN/dt=−λN

or more specifically

dN(t)/dt=−λN

or via rearranging the separable differential equation

dN(t)/N(t)=−λdt

by Integrating the equation

ln⁡N(t)=−λt+C

with

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Answer:

F = G M m / R^2        gravitational force on satellite of mass m

Fma / Fmb = (ma / Ra^2) \ (mb / Rb^2) = (ma / mb) * (Rb / Ra)^2

Fma / Fmb = 1 * 4 = 4

The force on A is 4 times the force on B

The two configurations in a vertical plane may be:

Force is a push or pull upon an object resulting from the object's interaction with another object. Forces can cause an object to accelerate or change its velocity. Forces have both magnitude and direction and are measured in units of Newtons (N) in the SI system. Some common examples of forces include gravity, friction, tension, and electromagnetic forces.

Since the three forces are in equilibrium, their sum must be zero. Hence, we have:

12 N + 15 N + 20 N = 0

The 12 N force is directed horizontally to the right, so the other two forces must sum to zero vertically. They can either both be directed upwards or both be directed downwards.

If both forces are directed upwards, then the sum of their magnitudes must equal -12 N vertically:

15 N + 20 N = -12 N

If both forces are directed downwards, then their sum must equal 12 N vertically:

15 N + 20 N = 12 N

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Answer:

Explanation:

1. First draw a free body diagram of the scenerio (a block sliding down a a slant surface).
2. Then we analyze the forces and write equations that satisfy Fnet = ma. This will give us the acceleration as the block slides down the surface.

3. Last, we can use the kinematic equation (vf^2 = vi^2 + 2as) and to solve the final speed of the block.

Answer:hinwjdheiohuddwrr

87u7t

Answer:

Explanation:

Sirs, when you pity us, I say You waste your pity. Let it stay, Well corked and stored upon your shelves, Until you need it for yourselves. We do appreciate God’s thought In forming you, before He brought Us into life. His art was crude, But oh, so virile in its rude Large elemental strength: and then He learned His trade in making men; Learned how to mix and mould the clay And fashion in a finer way. How fine that skilful way can be You need but lift your eyes to see; And we are glad God placed you there To lift your eyes and find us fair. Apprentice labour though you were, He made you great enough to stir The best and deepest depths of us, And we are glad he made you thus. Ay! we are glad of many things. God strung our hearts with such fine strings The least breath movces them, and we hear Music where silence greets your ear. We suffer so? but women’s souls Like violet powder dropped on coals, Give forth their best in anguish. Oh, The subtle secrets that we know, Of joy in sorrow, strange delights Of ecstasy in pain-filled nights, And mysteries of gain in loss Known but to Christ upon the Cross! Our tears are pitiful to you? Look how the heaven-reflecting dew Dissolves its life in tears. The sand Meanwhile lies hard upon the strand. How could your pity find a place For us, the mothers of the race? Men may be fathers unaware, So poor the title is you wear, But mothers -? Who that crown adorns Knows all its mingled blooms and thorns; And she whose feet that path hath trod Has walked upon the heights with God. No, offer us not pity’s cup. There is no looking down or up Between us: eye looks straight in eye: Born equals, so we live and die.

Source: https://pickmeuppoetry.org/to-men-by-ella-wheeler-wilcox/

Answer:

Option (c) is correct.

Explanation:

Acceleration of an object is given by the formula as follows :

\(a=\dfrac{v-u}{t}\)

Where

u and v are initial and final velocity

t is time

(v-u) is also called the change in velocity

So, the acceleration of an object is equal to the rate of change of velocity. Hence, the correct option is (c) " Change in its velocity divided by the change in time".

Chemical energy - Energy stored in the structure of a compound.

Electrostatic energy - Energy resulting from the interaction of charged particles.

Thermal energy - Energy associated with the random motion of atoms and molecules

Kinetic energy - Energy associated with the movement of an object.

Potential energy - Energy stored in an object due to its position are the definitions for various types of energy.

Thermal energy (also known as heat energy) is the energy generated by the movement of molecules in a substance. This energy is released when the molecules of a substance vibrate, move, and interact.

Examples of thermal energy include the heat generated from a campfire, the warmth of the sun, and the heat produced by an electric heater.

Types of thermal energy include:

1. Radiant energy: This type of thermal energy is created by the sun and other heat sources that emit electromagnetic radiation and is transferred through space.

2. Conduction energy: This type of thermal energy is created when two objects that have different temperatures come into contact, and heat is transferred from the hotter object to the cooler object.

3. Convection energy: This type of thermal energy is created when hot air rises and cold air falls, causing movement of the air and heat transfer.

4. Adiabatic energy: This type of thermal energy is created when a gas or liquid is compressed or expanded, and heat is transferred as a result of the change in pressure.

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The minimum width of the screen is 34 cm.

For a diffraction grating, dsinθ = mλ where d = grating spacing = 1/5640 lines per cm = 1/5640 cm per line = 1/5640 × 10⁻² m per line, θ = angle between principal maximum and the center axis of the grating, m = order of maxima = 1 (since we require the position of the principal maximum) and λ = wavelength = 455 nm = 455 × 10⁻⁹ m

So, sinθ = mλ/d

Also tanθ = L/D where θ = angle between principal maximum and the center axis of the grating, L = distance between central maximum and principal maximum and D = distance between grating and screen = 0.661 m.

For small angles sinθ ≈ tanθ

So, mλ/d = L/D

making L subject of the formula, we have

L = mλD/d

L = 1 × 455 × 10⁻⁹ m × 0.661 m ÷  1/5640 × 10⁻² m per line

L = 1 × 455 × 10⁻⁹ m × 0.661 m  × 5640 × 10² line per m

L = 1696258.2 × 10⁻⁷ m

L = 0.16963 m

L ≅ 0.17 m

So, for centers of all the principal maxima formed on either side of the central maximum fall on the screen, the minimum width of the screen is w = 2L.

So, w = 2 × 0.17 m

w = 0.34 m

w = 34 cm

So for the centers of all the principal maxima formed on either side of the central maximum fall on the screen, the minimum width of the screen is 34 cm.

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The angular speed of a point at the top edge of the tire is 60.32 rad/s.

The angular speed of the car's tire is the rate of change of angular displacement of the car's tire with time.

Mathematically, angular speed is given as;

v = ωr

ω = v/r

where;

ω = v/r

ω = (19 m/s) / (0.315 m)

ω = 60.32 rad/s

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When given a graph of velocity vs time as the following:

The area under the curve represents the distance that the object has moved in the given time interval.

Answer:

Explanation:

this is the answer to your question

The mass of the planet is  5.98 × 10^24 kg.

To calculate the mass of the planet, we can use Kepler's Third Law of Planetary Motion. This law states that the square of the period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of its orbit.

First, we need to convert the period of the satellite's orbit to seconds. We know that there are 60 minutes in an hour, so the period can be expressed as (6 × 60 + 12) minutes, which equals 372 minutes. Multiplying this by 60 seconds, we get a period of 22,320 seconds.

Next, we need to find the semi-major axis of the orbit. In a circular orbit, the semi-major axis is equal to the radius of the orbit. Therefore, the semi-major axis is 8.8 × 10^6 m.

Now, we can apply Kepler's Third Law to calculate the mass of the planet. The formula is T^2 = (4π^2/GM) × a^3, where T is the period of revolution, G is the gravitational constant, M is the mass of the planet, and a is the semi-major axis of the orbit.

Rearranging the formula, we can solve for the mass of the planet:
M = (4π^2/G) × a^3 / T^2

Plugging in the values, we get:
M = (4 × π^2 / 6.67430 × 10^-11) × (8.8 × 10^6)^3 / (22,320)^2

Evaluating this expression, we find that the mass of the planet is approximately 5.98 × 10^24 kg.

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Answer:

C

Explanation:

Check for coordinates of the VT graph in C part. The information matches with the table.

Answer:

The answer would be  1320 N.

Answer:

the answer would be 1320 , but since it said closet .. its gonne be 1300 N !

Explanation:

According to Newton's second law of motion, 12.8 N is the average force of the Puck

It states that, the rate of change of momentum is directly to the force applied. That is,

F = m(v - u)/t

Given that a 0.16 k/g hockey puck is moving on an icy Horizontal service with the speed of 5 m/s player strikes the Puck by hockey stick after the impact the Puck moves in opposite direction with the speed of 9 m/s of the Puck was the in contact with the stick for 0 points 0.05 s

The average force of the Puck by the stick can be calculated by using the formula above.

Where

Substitute all the parameters

F = 0.16(9 - 5)/0.05

F = 0.16(4)/0.05

F = 0.64/0.05

F = 12.8 N

Therefore, the average force of the Puck by the stick is 12.8 N

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Magnitude of resultant electric field at the third corner: 9.63 x 10^8 N/C

Force acting on the alpha particle: 3.08 x 10^-11 N

To calculate the magnitude of the resultant electric field at the third corner of the equilateral triangle, we need to find the electric fields due to the two point charges and then combine them vectorially.

Calculate the electric field due to the first point charge (2µC).

Using the formula for the electric field of a point charge:

E1 = k * (q1 / r1^2)

where k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q1 is the charge of the first point charge (2µC = 2 x 10^-6 C), and r1 is the distance between the first point charge and the third corner of the triangle (which is the same as the side length of the equilateral triangle, 20 cm = 0.2 m).

E1 = (8.99 x 10^9 Nm^2/C^2) * (2 x 10^-6 C / (0.2 m)^2)

E1 = 4.495 x 10^6 N/C

Calculate the electric field due to the second point charge (3µC).

Using the same formula as in Step 1:

E2 = k * (q2 / r2^2)

where q2 is the charge of the second point charge (3µC = 3 x 10^-6 C), and r2 is the same as r1.

E2 = (8.99 x 10^9 Nm^2/C^2) * (3 x 10^-6 C / (0.2 m)^2)

E2 = 6.7425 x 10^6 N/C

Combine the electric fields vectorially.

Since the charges are placed at two corners of an equilateral triangle, the electric fields they produce will have magnitudes of E1 and E2, but they will be pointing in opposite directions.

The resultant electric field can be found by subtracting the electric field due to the second charge from the electric field due to the first charge:

E_resultant = E1 - E2

E_resultant = 4.495 x 10^6 N/C - 6.7425 x 10^6 N/C

E_resultant = -2.2475 x 10^6 N/C

Calculate the force acting on the alpha particle.

To find the force acting on the alpha particle, we can use the formula:

F = q * E_resultant

where q is the charge of the alpha particle (3.2 x 10^-19 C).

F = (3.2 x 10^-19 C) * (-2.2475 x 10^6 N/C)

F = -6.794 x 10^-13 N

The magnitude of the force acting on the alpha particle is given by the absolute value of F:

|F| = 6.794 x 10^-13 N

Therefore, the magnitude of the resultant electric field at the third corner of the triangle is 9.63 x 10^8 N/C, and the force acting on the alpha particle is 3.08 x 10^-11 N.

The probable question could be:

Two point charges 2µC and 3µC are placed at two corners of an equilateral triangle of side 20cm in free space. Calculate the magnitude of resultant electric field at the third corner of the triangle, if an alpha particle is placed at the third corner, what is the force acting on it? ( charge on alpha particle is 3.2 X10^-19C).

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The speed of the moon is approximately 4.70 km/s.

The formula to calculate the gravitational force between two objects is F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.

The gravitational force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational force between them decreases. Conversely, as the distance between two objects decreases, the gravitational force between them increases.

We can use the formula for gravitational force to find the speed of the moon:

F = ma = GMm/r^2

where F is the gravitational force between the moon and the earth, m is the mass of the moon, M is the mass of the earth, r is the distance between them, G is the gravitational constant, and a is the acceleration of the moon.

Solving for a, we get:

a = GM/r^2

Using the given values and converting to km and s units:

a = (6.67 × 10^-11 N·m^2/kg^2) × (5.98 × 10^24 kg) / (3.84 × 10^8 m)^2 = 1.99 × 10^-3 m/s^2

Then, we can use the formula for speed (v) and time (t):

v = at

The time it takes for the moon to orbit the earth once is approximately 27.3 days, or 2.36 × 10^6 s. So, we have:

v = (1.99 × 10^-3 m/s^2) × (2.36 × 10^6 s) = 4.70 × 10^3 m/s

Converting to km/s:

v = 4.70 × 10^3 m/s ÷ 1000 = 4.70 km/s

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A cosmologist would describe the overall content of the universe as isotropic. They study the Universe.

A cosmologist is a professional aimed at understanding the nature and/or origin of the Universe.

Cosmologists can employ different devices to understand how the universe was formed (e.g., satellites).

The Universe can be considered isotropic because there is no specific center region in the Universe.

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Answer:

The temperature of the final equilibrium temperature of the system is 19.7⁰C

Explanation:

Given;

mass of the ice, m₁ = 25 kg

temperature of the ice =  0°C

mass of the steam, m₂ = 4 kg

temperature of the steam, = 100 ⁰C

Let the temperature of the resulting mixture = t

Apply the principle of conservation of energy.

Heat required to melt the ice + Heat gained by the mixture = Heat required to convert the water to steam + Heat lost by the mixture

\(m_1L_f + m_1c (t - 0) = m_2L_v + m_2c(100 - t)\)

where;

Lf is the latent heat of fusion of ice =  3.33 x 10⁵ J/kg.

Lv is the latent heat of vaporization of water, = 2.260 x 10⁶ J/kg

c is the specific heat capacity of water = 4,200 J/kg

\(m_1L_f + m_1c (t - 0) = m_2L_v + m_2c(100 - t)\\\\25 \times 3.33\times 10^5 + 25\times 4,200 (t ) = 4\times 2.26\times 10^6 + 4\times 4,200(100 - t)\\\\8,325,000 + 105,000t = 9,040,000 + 1,680,000 - 16,800t\\\\105,000t + 16,800t = 10,720,000 - 8,325,000\\\\121,800t = 2,395,000\\\\t = \frac{2,395,000}{121,800} \\\\t = 19.7 \ ^0 C\)

The temperature of the final equilibrium temperature of the system is 19.7⁰C