A rubber ball falls through 20 m (g=10 m/s²) onto the roof of an elevator ascending at 2 m/s. The impact is perfectly elastic. Find change in the ball's speed (m/s) during impact.
Physics · Mixed Chapter
JEE Main Practice

Question

A rubber ball falls through 20 m (g=10 m/s²) onto the roof of an elevator ascending at 2 m/s. The impact is perfectly elastic. Find change in the ball's speed (m/s) during impact.

G1 Physics · Accepted Answer

Step 1: Before impact, ball velocity is −√(2gh)=−20 m/s; elevator velocity is +2 m/s. Step 2: Relative incident velocity =−20−(+2)=−22 m/s. Step 3: Perfectly elastic collision with the effectively massive moving roof reverses relative velocity to +22 m/s. Ball's final ground velocity =+22+2=+24 m/s. Step 4: Initial speed 20 m/s, final speed 24 m/s. Change in speed =24−20=4 m/s. (Velocity change would be 44 m/s.)