A body is projected with a velocity $v_{1}$ from the point A as shown in the figure. At the same time, another body is projected vertically upwards from B with velocity $v_{2} .$ The point B lies vertically below the highest point. For both the bodies to collide, $\frac{v_{2}}{v_{1}}$ should be $\frac{1}{x}$ then $x$ = __________.

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Detailed Solution

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

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