First slide

Projection Under uniform Acceleration

Question

Two balls A and B are thrown with speeds u and u/2 respectively. Both the balls cover the same horizontal distance before returning to the plane of projection. If the angle of projection of ball B is 15^o with the horizontal, then the angle of projection of A is

Easy

A

$\sin^{- 1} (1 / 8)$
B

$\frac{1}{2} \sin^{- 1} (1 / 8)$
C

$\frac{1}{3} \sin^{- 1} (1 / 8)$
D

$\frac{1}{4} \sin^{- 1} (1 / 8)$

Solution

$\frac{u^{2} \sin 2 θ}{g} = \frac{(u / 2)^{2} \sin 30^{\circ}}{g} = \frac{u^{2}}{8 g}$
$∴ \sin 2 θ = 1 / 8 or 2 θ = \sin^{- 1} (1 / 8)$
or $θ = \frac{1}{2} \sin^{- 1} (1 / 8)$

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