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# A particle A is projected from the ground with an initial velocity of 10 m/s at an angle $60 ^{\circ}$ with horizontal. From what height h should another particle B be projected horizontally with velocity 5 m/s. so both the particle collide in the ground at point C if both are projected simultaneously $(g=10 m/s^2)$

$a)\;10 m \\b)\;30 m \\c)\;25 m \\ d)\;15 m$

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Horizontal component of velocity of A is $10 \cos 60 ^{\circ}=5 m/s$
The two will collide if time taken for both A and B to reach C is same
$t_A=t_B$
$h=\large\frac{1}{2}$$gt^2B$
$t_B=\sqrt {\large\frac{2h}{g}}$
$t_A=\large\frac{2u \sin \theta}{g}$
$\large\frac{2 u \sin \theta}{g}=\sqrt {\frac{2h}{g}}$
$h=\large\frac{2 u^2 \sin^2 \theta}{g}$
$\quad= \large\frac{2.10^2\bigg(\Large\frac{\sqrt 3}{2}\bigg)^2}{10}$
$\quad=15 m$
Hence d is the correct answer.

edited Jan 25, 2014 by meena.p

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