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

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+1 vote

+1 vote

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.

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