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Law Incorporation [45]

2 years ago

10

3. A horizontally moving tennis ball barely clears the net, a distance y above the surface of the court. To land within the tenn

is court the ball must not be moving too fast.
a. To remain within the court’s border, a horizontal distance d from the bottom of the net, show that the ball’s maximum speed over the net is v = / √ 2
b. Suppose the height of the net is 1.00 m, and the court’s border is 12.0 m from the bottom of the net. Use g = 10 m/s2 and show that the maximum speed of the horizontally moving ball clearing the net is about 27 m/s (about 60 mi/h).
c. Does the mass of the ball make a difference? Defend your answer.

1 answer:

maksim [4K]2 years ago

6 0

(a) The ball’s maximum speed over the net is v(max) = √2gh.

(b) The maximum speed of the horizontally moving ball clearing the net is about 27 m/s.

(c) Speed of the ball is independent of its mass.

<h3>Time of motion of the ball</h3>

The time of motion of the ball is calculated as follows;

h = vt + ¹/₂gt²

1 = 0 + ¹/₂(9.8)t²

1 = 4.9t²

t² = 1/4.9

t² = 0.204

t = 0.452 s

<h3>Horizontal speed of the ball</h3>

The horizontal speed of the ball is calculated as follows;

X = vt

v = X/t

v = (12 m)/(0.452)

v = 26.6 m/s ≈ 27 m/s (proved)

<h3>Conservation of energy</h3>

P.E = K.E

mgh = ¹/₂mv²

gh = ¹/₂v²

2gh = v²

√2gh = v(max)

Speed of the ball is independent of its mass.

Learn more about horizontal velocity here: brainly.com/question/24681896

#SPJ1

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Choose the option that best suit the question .

Igoryamba

Answer:

(b) 1/sinƟ

Explanation:

A simple machine can be defined as a type of machine with no moving parts but can be used to perform work.

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Inclined plane is a simple machine set at an angle and then used to lift an object.

In Physics, the velocity ratio of a simple machine is calculated as a ratio of the distance moved by the effort to the vertical distance through which a load is raised.

Mathematically, the velocity ratio of an inclined plane of angle Ɵ, acting as a simple machine is given by the formula;

Velocity ratio (V.R) = 1/sinƟ

Basically, an increase in the angle of inclination (measured in degrees) of an inclined plane increases its velocity ratio.

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3 years ago

A newly discovered planet has the same mass as the Earth, but a person standing on the surface of the planet experiences a force

Dafna11 [192]

This question deals with the acceleration due to gravity on the surface of the planet. The value of the acceleration due to gravity on the surface of two planets, that is Earth and on the surface of another planet are compared to find out the relation between the radii of both planets, provided their masses are the same.

The correct option for the radius of the new planet is "Option 3: Square Root of 3 R"

The value of the acceleration due to gravity on the surface of a planet is given by the following formula:

$g = \frac{GM}{R^2}$ ----------- eqn(1)

where,

g = acceleration due to gravity on Earth

G = Universal Gravitational Constant

M = mass of the Earth

R = Radius of the Earth

Now, the same formula for the acceleration due to gravity on the surface of the other planet can be written as follows:

$g' = \frac{GM'}{R'}\\\\$ ------------- eqn(2)

where,

g' = acceleration due to gravity on the new planet

G = Universal Gravitational Constant

M' = mass of the new planet

R' = Radius of the new planet

According to the given condition, the new planet has the same mass as the Earth's mass but the acceleration due to gravity on the surface of the new planet is one-third of the acceleration due to gravity on the surface of Earth.

$M'=M\\\\g'=\frac{1}{3}g$

using eqn (1) and eqn (2):

$\frac{GM}{R'^2}=\frac{1}{3}\frac{GM}{R^2}\\\\R'^2=3R^2\\\\R' = \sqrt{3}R$

Hence, the radius of the new planet is found to be equal to the square root of 3 times the radius of the Earth (Square Root of 3 R).

Learn more about acceleration due to gravity on the surface of a planet here:

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3 years ago

The specific heat of soil is 0.20 kcal/kg*C and the specific heat of water is 1.00 kcal/kg*C. This means that if 1 kg of soil an

stiv31 [10]

Answer: The soil will be $4\°C$ warmer than the water.

Explanation:

The heat (thermal energy) absorbed can be found using the following equation:

$Q=m.C.\Delta T$

Where:

$Q$ is the heat

$m$ is the mass of the element

$C$ is the specific heat capacity of the material.

$\Delta T$ is the variation in temperature

<u>In the case of soil we have:</u>

$Q_{soil}=m_{soil}.C_{soil}.\Delta T_{soil}$ (1)

Where:

$Q_{soil}=1 kcal$

$m_{soil}=1 kg$

$C_{soil}=0.2 kcal/kg \°C$

$\Delta T_{soil}$

<u>In the case of water we have:</u>

$Q_{water}=m_{water}.C_{water}.\Delta T_{water}$ (2)

Where:

$Q_{water}=1 kcal$

$m_{water}=1 kg$

$C_{water}=1 kcal/kg \°C$

$\Delta T_{water}$

Isolating $\Delta T$ from both equations:

$\Delta T_{soil}=\frac{Q_{soil}}{m_{soil}.C_{soil}}$ (3)

$\Delta T_{soil}=\frac{1 kcal}{1 kg(0.2 kcal/kg \°C)}$

$\Delta T_{soil}=5\°C$ (4)

$\Delta T_{water}=\frac{Q_{water}}{m_{water}.C_{water}}$ (5)

$\Delta T_{water}=\frac{1 kcal}{1 kg(1 kcal/kg \°C)}$

$\Delta T_{water}=1\°C$ (6)

Comparing (4) and (6) we can find the soil will be $4\°C$ warmer than the water.

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4 years ago

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mrs_skeptik [129]

You can write the equation in 3 different ways, depending on which quantity you want to be the dependent variable. Any one of the three forms can be derived from either of the other two with a simple algebra operation. They're all the same relationship, described by "Ohm's Law".

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==> Potential difference = (current) x (resistance)

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3 years ago

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Alisiya [41]

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3 years ago