Question

Suppose that a 112.5 kg football player running at 8.5 m/s catches a 0.44 kg ball moving at a speed of 25 m/s with his feet off the ground, while both of them are moving horizontally.

Calculate the change in kinetic energy of the system, in joules, after the player catches the ball.

Calculate the change in kinetic energy of the system, in joules, in this case.

Answer 1

Answer 2

To calculate the change in kinetic energy of the system, we need to find the initial kinetic energy (before catching the ball) and the final kinetic energy (after catching the ball) and then subtract the initial value from the final value.

1. Initial Kinetic Energy (before catching the ball): The initial kinetic energy of the football player can be calculated using the formula:

Initial Kinetic Energy = (1/2) * mass * velocity^2

For the football player: Mass (m1) = 112.5 kg Velocity (v1) = 8.5 m/s

Initial Kinetic Energy of the football player = (1/2) * 112.5 kg * (8.5 m/s)^2

2. Initial Kinetic Energy of the ball (before catching): The initial kinetic energy of the ball can be calculated using the same formula:

Initial Kinetic Energy = (1/2) * mass * velocity^2

For the ball: Mass (m2) = 0.44 kg Velocity (v2) = 25 m/s

Initial Kinetic Energy of the ball = (1/2) * 0.44 kg * (25 m/s)^2

3. Final Kinetic Energy (after catching the ball): After the football player catches the ball, both the player and the ball move together with the same horizontal velocity. So, we can consider them as one combined system with a total mass of:

Total Mass (m_total) = m1 + m2 Total Mass (m_total) = 112.5 kg + 0.44 kg

Now, the final velocity (v_final) of the combined system is the same as the initial velocity of the ball (25 m/s), since both are moving together horizontally after the catch.

Final Kinetic Energy = (1/2) * m_total * v_final^2

Final Kinetic Energy = (1/2) * (112.5 kg + 0.44 kg) * (25 m/s)^2

Now, we can calculate the change in kinetic energy:

Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy

Change in Kinetic Energy = [(1/2) * (112.5 kg + 0.44 kg) * (25 m/s)^2] - [(1/2) * 112.5 kg * (8.5 m/s)^2]

Calculate the values:

Change in Kinetic Energy = [0.5 * 112.94 kg * 625 m^2/s^2] - [0.5 * 112.5 kg * 72.25 m^2/s^2]

Change in Kinetic Energy ≈ 35143.75 J - 4505.31 J

Change in Kinetic Energy ≈ 30638.44 Joules

So, the change in kinetic energy of the system after the player catches the ball is approximately 30,638.44 Joules.