Question

A car is traveling on a highway at a speed of $25m/s$ 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 $10m/s$ 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, $\overrightarrow{v_c}=25\hat{i}$

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 ${\vec{v}}_{b/c}={\vec{v}}_b-{\vec{v}}_c$
$\Rightarrow {\vec{v}}_b={\vec{v}}_b+{\vec{v}}_{b/c}=25\hat{i}+6\hat{j}+8\hat{k}$