A ball of mass $0.15 ext{ kg}$ is dropped from a height $10 ext{ m}$, strikes the ground and rebounds to t

Question

A ball of mass $0.15 	ext{ kg}$ is dropped from a height $10 	ext{ m}$, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is ($g = 10 	ext{ m/s}^2$) nearly

Accepted Answer

Given that: Mass of ball = $0.15 	ext{ kg}$, Height from which ball is dropped = $10 	ext{ m}$. Impulse, $\vec{I} = 	ext{Change in linear momentum} = \Delta\vec{P} = \vec{P}_f - \vec{P}_i$. Velocity of ball at ground $(v) = \sqrt{2gh} = \sqrt{2 	imes 10 	imes 10} = 10\sqrt{2} 	ext{ m/s}$. $\vec{I} = 0.15 	imes 10\sqrt{2}(-\hat{j}) - 0.15 	imes 10\sqrt{2}(\hat{j}) = 2 	imes 0.15 	imes 10\sqrt{2}(-\hat{j}) = 4.2(-\hat{j})$. Magnitude of impulse = $4.2 	ext{ kg m/s}$.

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