Question

A car is travelling on a highway at a speed of 25 m/s along the 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 the car. What may be the initial velocity of the 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

The correct option is D

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

$u_x$ = $25\hat{i}$ as the car is moving with a speed of 25 $\frac{m}{s}$ along +ve axis, given $\theta ={37}^{\circ }$

$\therefore$$\frac{u_y}{u_z}=tan{37}^{\circ }=\frac{3}{4}$

$\therefore$ the only possible option is $25\hat{i}+6\hat{j}+8\hat{k}$.