Physics Vertical Kinematics

Question

Ball A is dropped at rest from height H and strikes the ground with speed V. Identical ball B is dropped from rest and strikes the ground with speed 2 V. From what height was ball B dropped? Answer in terms of H.

Answer 1

Let H₀ = the height from which the first ball is dropped, and V is its final velocity

Let H₁ = the height from which the 2nd ball is dropped, and W is its final velocity

In the first case, V² = V₀² + 2gH₀ = 2gH₀ because V₀ = 0.

In the 2nd case, W = 2V and W² = V₀² + 2gH₁ = 2gH₁ because V₀ = 0.

(2V)² = 2gH₁

Therefore,

H₁ = 4V² / 2g = 2V² / g