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 $