An athlete, swimming at a constant speed, covers a distance of 203 m in a time period of 5 minutes and 50 seconds. The drag force exerted by the water on the swimmer is 86.0 N. What is the power the swimmer must provide to overcome that drag force?

In order to solve this question, we will need to use kinematics

Let's see what is given to us:

Distance traveled is 137 meters

Time elapsed is 9.6 seconds

and inital velocity is 0 m/s

Since we are trying to find acceleration, we can use this formula

Where Δx is the distance traveled, v0 is the inital velocity, t is time, and a is acceleration

Plugging in what we have, we get

137 = 0(9.6) + 1/2(a)(9.6)^2

Solving for a, we get 2.97 m/s^2

The linear density of the string is 2.86 x 10^-5 kg/m.

What is linear density?

Linear density, also known as linear mass density, is a measure of the mass of a material per unit length. It is typically used to describe the properties of thin, elongated objects such as strings, wires, and fibers. The unit of measurement for linear density is typically kilograms per meter (kg/m) or grams per centimeter (g/cm). It is calculated by dividing the mass of the material by its length.

To find the linear density of the string, we need to use the relationship between the tension, linear density, and wave properties, which is given by the equation:

Tension = (linear density) * (wave speed)^2

where wave speed is the product of the frequency and wavelength of the wave.

Given the tension, period and wavelength, we can find the linear density using the following steps:

frequency = 1 / period = 1 / 3.82 x 10^-3 s = 261.9 Hz

wave speed = wavelength * frequency = 1.26 m * 261.9 Hz = 331.9 m/s

Tension = (linear density) * (wave speed)^2

944 N = (linear density) * (331.9 m/s)^2

linear density = Tension / (wave speed)^2 = 944 N / (331.9 m/s)^2 = 2.86 x 10^-5 kg/m

Therefore, the linear density of the string is 2.86 x 10^-5 kg/m.

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Answer: To calculate the magnitude of the resultant force exerted by the two tugboats on the barge, we can use vector addition. Since the towing lines are at an angle of 30° to each other, we can treat them as two vectors that form a triangle with the resultant force being the vector sum of the two towing forces.

Let's denote the towing force of the first tugboat as F1 = 3 kN, and the towing force of the second tugboat as F2 = 4 kN.

Using trigonometry, we can determine the horizontal and vertical components of the towing forces:

For F1:

Horizontal component: F1x = F1 * cos(30°)

Vertical component: F1y = F1 * sin(30°)

For F2:

Horizontal component: F2x = F2 * cos(30°)

Vertical component: F2y = F2 * sin(30°)

Now, we can add the horizontal and vertical components of the two towing forces separately to get the resultant force in the horizontal and vertical directions:

Horizontal component of resultant force: Fx = F1x + F2x

Vertical component of resultant force: Fy = F1y + F2y

Finally, we can use the Pythagorean theorem to calculate the magnitude of the resultant force:

Magnitude of resultant force: F = sqrt(Fx^2 + Fy^2)

Plugging in the values and calculating:

F1x = 3 kN * cos(30°) ≈ 2.598 kN

F1y = 3 kN * sin(30°) ≈ 1.5 kN

F2x = 4 kN * cos(30°) ≈ 3.464 kN

F2y = 4 kN * sin(30°) ≈ 2 kN

Fx = 2.598 kN + 3.464 kN ≈ 6.062 kN

Fy = 1.5 kN + 2 kN = 3.5 kN

F = sqrt(6.062 kN^2 + 3.5 kN^2) ≈ 6.964 kN

So, the magnitude of the resultant force exerted by the two tugboats on the barge is approximately 6.964 kN.

Total mass lost by the comet is 30.24 x 10¹⁰ kg.

Rate at which mass is lost, R = 35 x 10⁴ kg/s

Time period, T = 100 days = 8.64 x 10⁶s

Therefore,

Total mass lost by the comet, m = R x T

m = 30.24 x 10¹⁰ kg

So,

The fraction of loss = (30.24 x 10¹⁰)/(5 x 10¹⁵) = 60.48 x 10⁻⁵

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Answer:

A/A₀ = 0.5106

Explanation:

To do this, we need to use several formulas and expressions. First, we need to know the period of time of the oscillator. This can be calculated using the following expression:

ω = 2π/T   (1)

But angular frequency (ω) can be also be calculated using:

ω = √(k/m)   (2)

Using (1) and (2), we can solve for the period T:

2π/T = √(k/m)    (mass in kg)

2π/T = √(130/0.360)

2π/T = √361.11

2π/T = 19.003

T = 2π/19.003 = 0.331 s

Now, the amplitude A at a time t, is:

A = x exp(-bt/2m)    (3)

At time 0, A = x. so A₀ = x

The problem states that we have 11 cycles respect to the initial amplitude, so expression (3) can be rewritten as:

A = x exp(-b(17t/2m))     using b as kg/s = 0.086 kg/s

Replacing the data we have:

A = x exp(-0.086(17*0.331)/2*0.36)

A = x exp(-0.086 * 7.815)

A = x exp(-0.6721)

A = 0.5106x    (4)

Now, doing the ratio with the innitial we have:

A / A₀ = 0.5106x / x

The ratio is:

Hope this helps

Answer:

Two cars of equal weight and braking ability are travelling along the same road but combined with other factors it could mean the difference between life.

Answer:

Because the matter in solid objects doesn't move

Explanation:

Logic

1 mole of nitrogen atoms moving at 35.0 m/s possesses approximately 27.8 joules of energy.

To calculate the energy possessed by 1 mole of nitrogen atoms moving at 35.0 m/s, we need to consider both the kinetic energy and the molecular mass of nitrogen.

The kinetic energy (KE) of an object is given by the equation KE = 1/2 * m * v^2, where m is the mass and v is the velocity.

The molar mass of nitrogen (N₂) is approximately 28.0134 g/mol, which can be converted to kilograms by dividing by Avogadro's number (6.022 × 10^23). This gives us a mass of approximately 4.65 × 10^(-26) kg for one nitrogen atom.

Plugging in the values, we have KE = 1/2 * (4.65 × 10^(-26) kg) * (35.0 m/s)^2.

Evaluating the equation, we find that the kinetic energy possessed by one nitrogen atom is approximately 4.62 × 10^(-23) joules.

Since we are considering 1 mole of nitrogen atoms, we need to multiply this value by Avogadro's number to get the energy possessed by 1 mole. Avogadro's number is 6.022 × 10^23, so the total energy is approximately 2.78 × 10^1 joules, or 27.8 J.

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Answer:  I'm not sure, but I think it would be a total lunar eclipse

When the moon passes through the penumbra of Earth’s shadow it is referred to as partial lunar eclipse. The correct option is C.

A partial lunar eclipse occurs when the moon is not completely immersed in the umbra of the earth's shadow.

During a partial solar eclipse, the Moon, Sun, and Earth do not align perfectly straight, and the Moon casts only the penumbra of its shadow on Earth. From our vantage point, it appears that the Moon has eaten the Sun.

A shadow's penumbra is the lighter outer edge. Partial solar eclipses are caused by the Moon's penumbra, while penumbral lunar eclipses are caused by the Earth's penumbra. The penumbra is a type of lighter shadow.

The Penumbra is a half-shadow region that occurs when an object only partially covers a light source.

Thus, the correct option is C.

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If the rover is moving at a constant speed, then there is no net force acting on it and the rover is in equilibrium. In particular, Newton's second law says that

n + (-w) = 0   →   n = w

where n and w denote the magnitude of the normal force acting on the rover and its weight, respectively.

With a gravitational acceleration of 1.6 m/s², the rover's weight, and hence the magnitude of the normal force, is

w = n = (1100 kg) (1.6 m/s²) = 1760 N

Answer:

V = a t      velocity after time t

t = 33.1 / 9.80 = 3.38 sec   (time ball had been falling)

S = 1/2 a t^2 = 55.9 m

So the ball had been falling  for 7 * 8 = 56 m  

The child was 7 floors from the top

Since he was on the eight floor the floors below him were

7 * 8 + 12 = 68 m     total floors below child

68 + 56 = 124 m      total height of building

Total floors in building = 7 + 7 + 1 = 15 floors

PE at top = KE at bottom

KE = m g h = .125 * 9.80 * 124 = 152 Joules

Answer:

About 1000 miles.

Explanation:

Answer:

His velocity when t= 3 sec is V= 1.56 m/s

Explanation:

a= 0.5 m/s²

ω= 0.2 rad/s

t= 3 sec

Vr= a*t

Vr= 1.5 m/s

r= a*t²/2

r= 2.25m

Vt= w*r

Vt= 0.45 m/s

V= √(Vr²+Vt²)

V= 1.56 m/s

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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Answer:

The area under the speed - time graph denotes the distance travelled by the object

In the given graph, we just have to think about the first 4 seconds, we also notice that the velocity at 4 seconds is 20 m/s

The distance travelled by the object in 4 seconds is the area of the triangle in the graph with a base of 4 units and height of 20 units (image included)

Distance Travelled = Area of triangle =  1/2 * base * height

Distance Travelled = 1/2 * 4 * 20

Distance travelled = 4 * 10

Distance travelled = 40 m

Given

The mass is m=1040 kg

The speed is v=7.2 m/s

To find

The momentum of the car.

Explanation

We know,

the momentum is given by

Putting the values,

Conclusion

The momentum is

Answer:

-240

Explanation:

A motorcycle skids for a distance of 2.0 m on an icy road, then the change in kinetic energy for the motorcycle will be equal to -240 J.

The force which a moving object has is referred to as kinetic energy in physics. It is defined as the number of effort required to propel a person of a specific mass from still to a specific velocity.

Aside from slight fluctuations in speed, your body holds onto the kinetic energy it obtains during acceleration.

When the body slows down from its present level to a condition of rest, the same quantity of energy is used.

Formally, kinetic energy is any quantity that has a gradient concerning time in the Lagrangian of a system.

As per the given information in the question,

Distance, d = 2.0 m

Friction, f = 120 N

The angle between displacement and friction force, θ = 180°

Now, the change in kinetic energy for the motorcycle = Work done by the friction.

K.E = f × d(cos θ)

= 120 (2.0 m)(cos 180°)

Δ K.E = -240 J

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A rope pulls a Tesla out of mud. The guy pulls a force F⊥ of 300N, and theta = 4.2°. The tension force T is 298.44__ Newton.

The problem describes a Tesla that is stuck in the mud and needs to be pulled out using a rope. the guy pulls a force F⊥ of 300N and that the angle between the rope and the horizontal plane is θ = 4.2°. The goal is to find the tension force T exerted by the rope.To solve for T, we'll need to use trigonometry. We can break the force vector into its horizontal and vertical components as follows:

Fx = F⊥ cosθ and Fy = F⊥ sinθ.

Since the rope is pulling the Tesla horizontally, the horizontal component of the force will be the tension force T. So we have:

T = Fx = F⊥ cosθ = (300 N) cos(4.2°) ≈ 298.44 N

Taking the cosine of the angle is necessary since it's the adjacent side that we're interested in, which is the horizontal component of the force. Therefore, the tension force exerted by the rope is approximately 298.44 N.

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If the material's physical characteristics and other factors are constant, doubling the wall's thickness will reduce its thermal conductivity by a factor of two.

The capacity of a material to conduct heat is known as thermal conductivity.

When a wall's thickness doubles, there is now a twofold increase in the amount of material that heat must pass through to move from one side to the other of the wall. This denotes a reduction in thermal conductivity due to a slowing of heat transfer.

Therefore,  If the material's physical characteristics and other factors are constant, doubling the wall's thickness will reduce its thermal conductivity by a factor of two.

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Answer:

An object that isn't moving?

Answer:

(C) apparently written incorrectly - it should be 29.9 +- .3 K

(read 29.9 plus or minus .3 K)

Answer:

Dark matter:

- Doesn't interact with baryonic matter.

- It has not been observed directly

- dark matter does not absorb, reflect or even emit light, thereby making it to be extremely hard to spot. Therefore, it does not interact with electromagnetic radiation.

Explanation:

Dark matter:

- Doesn't interact with baryonic matter.

- It has not been observed directly

- dark matter does not absorb, reflect or even emit light, thereby making it to be extremely hard to spot. Therefore, it does not interact with electromagnetic radiation.

Baryonic matter:

- Has been observed directly because it includes nearly all the matter that we see in the world daily.

- It interacts with baryonic matter

- interacts with electromagnetic radiation

Dark Matter:

Baryonic Matter:

Dark matter can be defined as often invisible substances that are difficult to spot because they don't absorb, emit or reflect light.

Hence, dark matter do not affect human view because they do not interact or interfere with electromagnetic radiation (force).

Although, humans can see right through the (weakly interacting) dark matter but it has not been observed directly.

Baryonic matter can be defined as a dark matter that is made up of baryons such as neutrons, and protons. Also, they are ordinary matter (both fermions and hadrons), as distinct from exotic forms.

In conclusion. baryonic matter has been observed directly and it can interact with electromagnetic radiation.

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Answer:

Motor cortex

Both hemispheres have a motor cortex, with each side controlling muscles on the opposite side of the body (i.e, the left hemisphere controls muscles on the right side of the body).

Explanation:

Answer:

13.75m/s; 42.2m; 8s

Explanation:

(a) the car's velocity after 2.50 s is 13.75 m/s

(b) The distance traveled by the car is 42.18 m

(c)  the time taken for the car to come to complete stop is 8 s.

The given parameters;

mass of the car, m = 2500 kg

initial velocity of the car, u = 20 m/s

breaking applied on the car, f = 6250 N

The acceleration of the car is calculated as follows;

\(F = ma \\\\a = \frac{F}{m} = \frac{6250}{2500} = 2.5 \ m/s^2\)

(a) Using impulse-momentum theorem, the car's velocity after 2.5 s is calculated as follows;

\(F = \frac{m(u-v)}{t} \\\\m(u-v) = Ft\\\\u-v = \frac{Ft}{m} \\\\v = u - \frac{Ft}{m} \\\\v = 20 - \frac{6250 \times 2.5}{2500} \\\\v = 13.75 \ m/s\)

(b) The distance traveled by the car during the 2.5 s;

\(v^2 = u^2 - 2as\\\\2as = u^2 - v^2\\\\s = \frac{u^2 - v^2}{2a} \\\\s = \frac{20^2 - 13.75^2}{2\times 2.5} \\\\s = 42.18 \ m\)

(c) The time taken for the car to come to a complete stop;

when the car stop's the final velocity, v = 0

v = u - at

0 = 20 - 2.5t

2.5t = 20

\(t = \frac{20}{2.5} \\\\t = 8 \ s\)

Thus, the time taken for the car to come to complete stop is 8 s.

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Answer:

A fluid that has properties, such as a large and uniform thermal expansion coefficient, good thermal conductivity, and chemical stability, that make it suitable for use in a thermometer. Thermometric liquids are those that are used in thermometers. Some examples of such liquids are mercury and alcohol.

Explanation:

Answer:

a thermometric liquid is a liquid which can change its temperature in accordance woth temperature. it is used to measure temperature.For example: alcohol and mercury

The statement that best describes the production of energy in the Sun is nuclei with less mass combine to form nuclei with more mass in the Sun’s core and release energy.

Sun is a major source of renewable energy to the Earth. This energy serves various purposes by living organisms.

However, the energy is generated as a result of nuclear fusion, which is the combination of smaller particles to form a larger one.

Therefore, the statement that best describes the production of energy in the Sun is nuclei with less mass combine to form nuclei with more mass in the Sun’s core and release energy.

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Answer:

W = F • ∆x

so for work to be done, a force and displacement has to be in the same direction. (Ex: a box is being pushed forward and it's also moving forward.)

Answer:

The depth of the resulting stream is 3.8 meters.

Explanation:

Under the assumption that streams are formed by incompressible fluids, so that volume flow can observed conservation:

\(\dot V_{1} + \dot V_{2} = \dot V_{3}\) (1)

All volume flows are measured in cubic meters per second.

Dimensionally speaking, we can determine the depth of the resulting stream (\(h_{3}\)), in meters, by expanding (1) in this manner:

\(w_{1}\cdot h_{1}\cdot v_{1} + w_{2}\cdot h_{2}\cdot v_{2} = w_{3}\cdot h_{3}\cdot v_{3}\)

\(h_{3} = \frac{w_{1}\cdot h_{1}\cdot v_{1}+w_{2}\cdot h_{2}\cdot v_{2}}{w_{3}\cdot v_{3}}\) (2)

\(v_{1}, v_{2}\) - Speed of the merging streams, in meters per second.

\(h_{1}, h_{2}\) - Depth of the merging streams, in meters.

\(w_{1}, w_{2}\) - Width of the merging streams, in meters.

\(w_{3}\) - Width of the resulting stream, in meters.

\(v_{3}\) - Speed of the resulting stream, in meters per second.

If we know that \(w_{1} = 8.3\,m\), \(h_{1} = 3.2\,m\), \(v_{1} = 2.2\,\frac{m}{s}\), \(w_{2} = 6.8\,m\), \(h_{2} = 3.2\,m\), \(v_{2} = 2.4\,\frac{m}{s}\), \(w_{3} = 10.4\,m\) and \(v_{3} = 2.8\,\frac{m}{s}\), then the depth of the resulting stream is:

\(h_{3} = \frac{(8.3\,m)\cdot (3.2\,m)\cdot \left(2.2\,\frac{m}{s} \right) + (6.8\,m)\cdot (3.2\,m)\cdot \left(2.4\,\frac{m}{s} \right)}{(10.4\,m)\cdot \left(2.8\,\frac{m}{s} \right)}\)

\(h_{3} = 3.8\,m\)

The depth of the resulting stream is 3.8 meters.

Answer:

naruto and hinata

Explanation: