A rubber ball is released from height 5 m above the floor. It bounces repeatedly, each time rising to 81/100 of the height through which it fell. Find its average speed. Take g=10 m s⁻².
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Question

A rubber ball is released from height 5 m above the floor. It bounces repeatedly, each time rising to 81/100 of the height through which it fell. Find its average speed. Take g=10 m s⁻².

G1 Physics · Accepted Answer

Initial drop height is 5 m, so first fall time is 1 s. Rebound heights form 5(0.81)ⁿ, and their square roots form factor 0.9. Total distance =5+2×5[0.81/(1-0.81)]=47.6316 m. Total time =1+2[0.9/(1-0.9)]=19 s. Average speed =47.6316/19≈2.50 m s⁻¹. Hence option A.