A ball is dropped from a height of 16 m. After each bounce it rises to half the height from which it fell. Find the total vertical distance travelled before it effectively comes to rest, in metres.
Physics · Mathematical tools and vector · Sequence & Series
NEET JEE Mains

Question

A ball is dropped from a height of 16 m. After each bounce it rises to half the height from which it fell. Find the total vertical distance travelled before it effectively comes to rest, in metres.

G1 Physics · Accepted Answer

Initial fall=16 m. Rebound heights form 8+4+2+... with sum 8/(1−1/2)=16 m. Each rebound height is travelled upward and downward, so total=16+2×16=48 m.