12th grade physics ap question.
A baseball with a mass of 120 g is hit 21.8 m into the air. The ball is caught by the third baseman 2.5 m above the ground. What potential energy did the ball develop at its highest point? How much potential energy did it still have when it was caught? What kinetic energy did it have when it was caught? At what velocity did it strike the player's mitt?
PEhightest: mgh
PE at catch: mgh
For the last two, you have to know more, like the angle it was hit at. Lets assume then it had no horizontal velocity, so all KE was vertical velocity. KE caught then is the difference between PE hightest and PE caught mg(21.8-2.5)
Velocity with this same assumption 1/2 m v^2=KEat impact
okay that makes sense thanks.
To find the potential energy developed by the baseball at its highest point, we can use the formula for gravitational potential energy (GPE):
GPE = mgh
Where:
m = mass of the baseball (120 g = 0.12 kg)
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height of the baseball at its highest point (21.8 m)
Substituting these values into the formula:
GPE = (0.12 kg)(9.8 m/s²)(21.8 m)
GPE = 26.8496 J
Therefore, the potential energy developed by the baseball at its highest point is approximately 26.85 J.
To calculate the potential energy the ball still had when it was caught, we need to consider its height above the ground at that point. The height above the ground is given as 2.5 m.
Potential energy when caught = mgh
Substituting the values:
Potential energy when caught = (0.12 kg)(9.8 m/s²)(2.5 m)
Potential energy when caught = 2.94 J
Therefore, the potential energy the ball still had when caught is approximately 2.94 J.
To calculate the kinetic energy of the ball when it was caught, we need to know its velocity at that point. However, this information is not given. Therefore, we cannot determine the kinetic energy.
Finally, to calculate the velocity at which the ball struck the player's mitt, we can consider the conservation of energy. At its highest point, all of the ball's potential energy is converted to kinetic energy.
Potential energy at the highest point = Kinetic energy when caught
Setting up the equation:
mgh = (1/2)mv²
Canceling out the mass, we get:
gh = (1/2)v²
Rearranging the equation to solve for velocity:
v = √(2gh)
Substituting the values:
v = √(2)(9.8 m/s²)(2.5 m)
v = √(49) m/s
v ≈ 7 m/s
Therefore, the velocity at which the ball struck the player's mitt is approximately 7 m/s.
To find the potential energy developed by the baseball at its highest point, we need to use the formula for gravitational potential energy:
Potential energy = mass × gravitational acceleration × height
Given:
mass of the ball (m) = 120 g = 0.12 kg
height (h) = 21.8 m
The gravitational acceleration (g) near the Earth's surface is approximately 9.8 m/s^2.
Potential energy at the highest point:
Potential energy = 0.12 kg × 9.8 m/s^2 × 21.8 m
To find the potential energy the ball had when it was caught by the third baseman, we need to consider its height at that point. Since the ball was caught 2.5 m above the ground, the height would be:
height (h) = 21.8 m - 2.5 m
Potential energy when caught:
Potential energy = 0.12 kg × 9.8 m/s^2 × (21.8 m - 2.5 m)
To calculate the kinetic energy of the ball when it was caught, we need to apply the conservation of energy principle. The total energy at any point remains constant, so we can subtract the potential energy from the total mechanical energy to find the kinetic energy.
Total mechanical energy = potential energy + kinetic energy
Since the ball was caught, its potential energy is the maximum, and its kinetic energy is zero. Therefore, the potential energy when caught is equal to the total mechanical energy at that point.
To find the velocity at which the ball struck the player's mitt, we can use the equation for kinetic energy:
Kinetic energy = 0.5 × mass × velocity^2
Since we know the mass of the ball (0.12 kg) and the potential energy when it was caught (which is equal to the kinetic energy), we can rearrange the equation to solve for velocity:
Velocity = sqrt((2 × kinetic energy) / mass)
Substituting the values, we can find the velocity at which the ball struck the player's mitt.