Understanding Impulse

Impulse is the change in momentum of an object. It's represented by the equation:

* Impulse (J) = Δp = m * Δv

Where:

* J is impulse

* Δp is the change in momentum

* m is mass

* Δv is the change in velocity

Solving the Problem

1. Initial Momentum: The ball's initial momentum is:

* p_initial = m * v_initial = 20 kg * 7 m/s = 140 kg m/s

2. Final Momentum: Since the ball rebounds elastically at the same speed, its final velocity is -7 m/s (negative since it's moving in the opposite direction).

* p_final = m * v_final = 20 kg * (-7 m/s) = -140 kg m/s

3. Change in Momentum: The change in momentum is:

* Δp = p_final - p_initial = -140 kg m/s - 140 kg m/s = -280 kg m/s

4. Impulse: The impulse given to the wall is equal to the change in momentum of the ball:

* Impulse (J) = Δp = -280 kg m/s

Important Note: The negative sign indicates that the impulse is in the opposite direction of the ball's initial motion. This means the wall experiences a force that pushes the ball back.

Therefore, the amount of impulse given to the wall is 280 kg m/s.