A car is traveling on a highway at a speed of 25 m/s along x-axis. A passenger in a car throws a ball at an angle 37^owith horizontal in a plane perpendicular the motion of the car. The ball is projected with a speed of 10 m/s relative to car What may be the initial velocity of ball in unit vector notation

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$25 \hat{i} + 8 \hat{j} + 6 \hat{k}$

$10 \hat{i} + 8 \hat{j} + 6 \hat{k}$

$10 \hat{i} + 25 \hat{j} + 6 \hat{k}$

$25 \hat{i} + 6 \hat{j} + 8 \hat{k}$

answer is D.

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Detailed Solution

Velocity of the car, $\vec{v_{c}} = 25 \hat{i}$

Velocity of ball with respect to car

$\begin{array}{l} {\vec{v}}_{b / c} = u \sin 37^{\circ} \hat{j} + u \cos 37^{\circ} \hat{k} \\ = 10 \times \frac{3}{5} \hat{j} + 10 \times \frac{4}{5} \hat{k} = 6 \hat{j} + 8 \hat{k} \end{array}$

$Now: using {\vec{v}}_{b / c} = \vec{v_{b}} - {\vec{v}}_{c}$

$\vec{v_{b}} = \vec{v_{b}} + {\vec{v}}_{b / c} = 25 \hat{i} + 6 \hat{j} + 8 \hat{k}$

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