Question

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 $37^{\circ}$ with 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?

• A. $25 \hat{i}+8 \hat{j}+6 \hat{k}$
• B. $10 \hat{i}+8 \hat{j}+6 \hat{k}$
• C. $10 \hat{i}+25 \hat{j}+6 \hat{k}$
• D. $25 \hat{i}+6 \hat{j}+8 \hat{k}$

Answer 1

Answer: (D)

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

Velocity of ball with respect to car
$\vec{v}_{b / c} =u \sin 37^{\circ} \hat{j}+u \cos 37^{\circ} \hat{k} $
$=10 \times \frac{3}{5} \hat{j}+10 \times \frac{4}{5} \hat{k}=6 \hat{j}+8 \hat{k}$
Now: using $\vec{v}_{b / c}=\vec{v}_{b}-\vec{v}_{c}$
$\Rightarrow \vec{v}_{b}=\vec{v}_{b}+\vec{v}_{b / c}=25 \hat{i}+6 \hat{j}+8 \hat{k}$