A ball is dropped from a height H. After every collision with the ground, it rises to half the previous height. If the total vertical distance travelled before coming to rest is 60 m, find H in metres.
Physics · Mathematical tools and vector · Sequence & Series
NEET JEE Mains

Question

A ball is dropped from a height H. After every collision with the ground, it rises to half the previous height. If the total vertical distance travelled before coming to rest is 60 m, find H in metres.

Physics · Mathematical tools and vector · Sequence & Series

G1 Physics · Accepted Answer

Initial fall=H. Rebound heights H/2+H/4+... have sum H. Since each rebound height is travelled up and down, total distance=H+2H=3H. Thus 3H=60 and H=20 m.