A ball hits a wall and rebounds with the same speed it had before. What does this tell you about the impulse?

Question

BlackTom AI · Accepted Answer

Consider the situation: a ball hits a wall and rebounds with the same speed, meaning its velocity vector reverses in direction but its magnitude remains unchanged. 
Option a: The force was perpendicular to the motion. While a force perpendicular to the velocity can change the direction of motion, the impulse associated with a bounce primarily changes the momentum's direction along the line of impact; this choice doesn’t directly address the momentum change required by the rebound with equal speed. In short, this statement is not the best description of the impulse in a wall bounce with equal speed. 
Option b: Momentum increased. Momentum magnitude stays the same in this scenario (speed is unchanged) but its direction reverses, so there is no net increase in the magnitude of momentum. This makes this option incorrect. 
Option c: Impulse reversed the ball’s momentum. This is the correct reasoning: impulse equals the change in momentum, Δp = p_final − p_initial. If p_initial = mv to the right and p_final = mv to the left (equal magnitude, opposite direction), then Δp = (−mv) − (mv) = −2mv, so the impulse is nonzero and directed to reverse the momentum. The impulse is effectively responsible for flipping the momentum’s direction. 
Option d: Impulse was zero. A zero impulse would mean no change in momentum, which contradicts the observed reversal of motion. Therefore this option is false.

A ball hits a wall and rebounds with the same speed it had before. What does this tell you about the impulse?Single choice

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