A soccer ball of mass 250 text{ g} is moving | vedclass

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(C) Given: Mass $m = 250 	ext{ g} = 0.25 	ext{ kg} = \frac{1}{4} 	ext{ kg}$.Initial velocity $\vec{u} = -22 \hat{i} 	ext{ ms}^{-1}$.Final velocity

Vedclass · Accepted Answer

$1166$

Vedclass · Answer

(C) Given: Mass $m = 250 	ext{ g} = 0.25 	ext{ kg} = \frac{1}{4} 	ext{ kg}$.Initial velocity $\vec{u} = -22 \hat{i} 	ext{ ms}^{-1}$.Final velocity $\vec{v} = 30 \cos 53^{\circ} \hat{i} + 30 \sin 53^{\circ} \hat{j} = 30(\frac{3}{5}) \hat{i} + 30(\frac{4}{5}) \hat{j} = 18 \hat{i} + 24 \hat{j} 	ext{ ms}^{-1}$.Change in momentum $\Delta \vec{P} = m(\vec{v} - \vec{u}) = \frac{1}{4} [(18 \hat{i} + 24 \hat{j}) - (-22 \hat{i})] = \frac{1}{4} [40 \hat{i} + 24 \hat{j}] = 10 \hat{i} + 6 \hat{j} 	ext{ Ns}$.Magnitude of change in momentum $|\Delta \vec{P}| = \sqrt{10^2 + 6^2} = \sqrt{100 + 36} = \sqrt{136} 	ext{ Ns}$.Average force $\vec{F}_{avg} = \frac{\Delta \vec{P}}{\Delta t} = \frac{\sqrt{136}}{0.01} = 100 \sqrt{136} \approx 100 	imes 11.66 = 1166 	ext{ N}$.

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