First slide

Collisions

Question

A ball of mass m falls vertically to the ground from a height h₁ and rebound to a height h₂. The change in momentum of the ball on striking the ground is

Moderate

A

$mg (h_{1} - h_{2})$
B

$m (\sqrt{2 {gh}_{1}} + \sqrt{2 {gh}_{2}})$
C

$m \sqrt{2 g (h_{1} + h_{2})}$
D

$m \sqrt{2 g} (h_{1} + h_{2})$

Solution

When ball falls vertically downward from height h₁ its velocity $|{\vec{v}}_{1}| = \sqrt{2 {gh}_{1}}$
and its velocity after collision $|{\vec{v}}_{2}| = \sqrt{2 {gh}_{2}}$
Change in momentum
$|Δ \vec{P}| = |m ({\vec{v}}_{2} - {\vec{v}}_{1})| = m (\sqrt{2 {gh}_{1}} + \sqrt{2 {gh}_{2}})$
(because ${\vec{v}}_{1}$ and ${\vec{v}}_{2}$ are opposite in direction)

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