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A particle A is projected with an initial velocity of 60 m/s at an angle $30 °$ 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 angle of projection $α$ of particle B.

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$37 °$

$47 °$

$42 °$

$52 °$

answer is A.

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Detailed Solution

$u_{A y} = 60 \sin 30 ° = 30 m / s and u_{B y} = 50 \sin α$

The two particles will collide, if their relative velocity $v_{A B}$ is along the line joining A and B. This is possible only when

$u_{A y} = u_{B y}$

i.e. components of velocity along y-axis are same for both particles.

$∴ 30 = 50 \sin α or, α = \sin^{- 1} (3 / 5) = 37 °$

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