Question

A body is projected with velocity $v_1$ from the point $A$ as shown in Fig. At the same time, another body is thrown vertically upward from $B$ with velocity $v_2$. Point B lies vertically below the highest point. For both the bodies to collide, $\frac{v_2}{v_1}$ should be

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

Answer 1

Answer: (A)

$\frac{1}{2}$

Refer image.

for collision at highest point, the vertical velocity at the time of projection is equal for both bodies.

$v_1\sin {30}^0=v_2$

$\Rightarrow \frac{v_1}{v_2}=\frac{1}{\sin {30}^0}$

$\Rightarrow \frac{v_2}{v_1}=\sin {30}^0$

$\frac{v_2}{v_1}=\frac{1}{2}$