Question

A ball of mass m is thrown straight upward from ground level at speed v0. At the same instant, at a distance D above the ground, another ball of mass m is thrown straight downward toward the first ball, also at speed v0. Assume that gravity acts vertically downward on each mass m with a magnitude mg. v0 D b How far above the ground do the balls collide (in terms of only D, v0, and g)?

Answer 1

Step-by-step explanation:

Let the balls collide after time t .

distance covered by falling ball

s₁ = v₀ t + 1/2 g t²

distance covered by rising ball

s₂ = v₀ t - 1/2 g t²

Given ,

s₁ + s₂ = D

D = v₀ t + 1/2 g t² + v₀ t - 1/2 g t²

= 2v₀ t

t = D / 2v₀

s₂ = v₀ t - 1/2 g t²

= v₀ x D / 2v₀ - (1/2) x g x D² / 4v₀²

= D / 2 - gD² / 8 v₀²