Question

A body is projected with velocity ${\upsilon }_1$ from the point A, another body at the same time is projected vertically upwards from B with velocity 1:2 as shown in adjoining figure. If the point B lies vertically below the highest point C, then for both bodies to collide the ratio $\frac{{\upsilon }_2}{{\upsilon }_1}$ should be

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

Answer 1

Answer: (A)

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