Question

A body is projected with velocity $v_1$ from the point $A$, another body at the same time is projected vertically upwards from $B$ with velocity $v_2$ as shown in adjoining figure. If the point $B$ lies vertically below the highest point $C$, then for both bodies to collide the ratio $\frac{v_2}{v_1}$ should be

• A. $0.5$
• B. $1$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{2}{\sqrt{3}}$

Answer 1

The correct option is A $0.5$

The two bodies will collide at the highest point if both cover the same vertical height in the same time.
So, $\frac{v_1^2{\sin }^2{30}^{\circ }}{2g}=\frac{v_2^2}{2g}$
or $\frac{v_2^2}{v_1^2}={\sin }^2{30}^{\circ }$
$\Rightarrow \frac{v_2}{v_1}=\sin {30}^{\circ }=\frac{1}{2}=0.5$.