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Applications of Relative Projectile

A particle A ...

Question

A particle A is projected with an initial velocity of $60$ m/s at an angle $30^{o}$ to the horizontal. At the same time a second particle B is projected in opposite direction with initial speed of $50$ m/s from a point at a distance of $100$ m from A. If the particles collide in air, find the distance of P from A, where collision occurs. $(g = 10 m / s^{2})$ .

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Solution

$u A x = 60 cos 30^{o} = 30 \sqrt{3} \frac{m}{s}$
$u A y = 60 sin 30^{o} = 30 \frac{m}{s}$
$u B x = - 50 cos α$
$u B y = 50 sin α$
A and B reach the same height at same time condition for collision
$u A y = u B y$
$30 = 50 s i n α$
$α = {s i n}^{- 1} \frac{3}{5}$

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