A ball was thrown from height $H$ and the ball hit the floor with velocity $10 (\hat{i} - \hat{j})$ after $1.5 s e c$ of its projection. Find initial speed of ball.

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$10 \sqrt{5} m / s$

$5 \sqrt{5} m / s$

$15 m / s$

$30 m / s$

answer is B.

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Detailed Solution

$v_{x} = 10 \hat{i} v_{y} = - 10 \hat{j} t = 1.5 s e c a = - g \hat{j} = - 10 \hat{j}$

$(\vec{u_{y}}) = - 10 \hat{j} - (- 10 \hat{j}) \times (1.5) \Rightarrow (\vec{u_{y}}) = 5 \hat{j} \vec{u} = 10 \hat{i} + 5 \hat{j} \Rightarrow |\vec{u}| = 5 \sqrt{5} m / s$

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