# A ball $B_1$ is projected from A at a velocity u making an angle $30 ^{\circ}$with the horizontal. Another ball $B_2$ is simultaneously projected from C verically up and with velocity v.Both collide each other at their maximum heights. What is ratio $\large\frac{u}{v}$

$a)\;4 \\b)\;2 \\c)\;1 \\ d)\;0.5$

For Ball $B_2 : 0-v^2=-2gh$
$h=\large\frac{v^2}{2g}$
For Ball $B_1$ to reach the same height the vertical component of velocity is $u \sin \theta=u \sin 30$
$\quad \qquad= u/2$
Therefore $\large\frac{-u^2}{4}$$=-2g\bigg(\large\frac{v^2}{2g}\bigg) \qquad=\large\frac{u^2}{v^2} \qquad=4 \quad\large\frac{u}{v}$$=2$
Hence b is the correct answer.
edited May 24, 2014

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