Which ball is subjected to the greater magnitude of impulse during its collision with the floor?

Question

Two equal mass balls (one red and the other green) are dropped from the same height, and rebound off the floor. The red ball rebounds to a higher position. Which ball is subjected to the greater magnitude of impulse during its collision with the floor?

A) It’s impossible to tell since the time intervals and forces are not known.

B) Both balls were subjected to the same magnitude impulse.

C) The green ball.

D) The red ball.

Why is the answer D)?

Answer 1

In general, impulse is equal to change in momentum, which can be written as

mv₂ - mv_1, where

m is the mass of the ball,

v₁ is the velocity before impact,

v₂ is the velocity before impact.

(It is important to treat both velocities as vectors.)

The red ball experiences greater change in momentum, because

1. Both balls have the mass m,
2. Both ball have the same velocity v₁, as they fell from the same height,
3. The red ball has greater velocity v₂, as it rebounded to a greater height.