First slide

Projection Under uniform Acceleration

Question

A particle is projected with a certain velocity at an angle $α$ above the horizontal from the foot of an inclined plane of inclination $30^{0}$ . If the particle strikes the plane normally then $α$ is equal to:

Moderate

A

$30^{0} + \tan^{- 1} (\frac{\sqrt{3}}{2})$
B

$45^{0}$
C

$60^{0}$
D

$30^{0} + \tan^{- 1} (\frac{2}{\sqrt{3}})$

Solution

$t_{AB} = time of flight of projectile$
= $\frac{2 u \sin (α - 30^{0})}{g \cos 30^{0}}$
Now component of velocity along the plane becomes zero at point B.
$θ = u \cos (α - 30^{0}) - g \sin 30^{0} \times T$
or $u \cos (α - 30^{0})$
= g sin $30^{0} \times \frac{2 u \sin (α - 30^{0})}{g \cos 30^{0}}$
or $\tan (α - 30^{0}) = \frac{\cot 30^{0}}{2} = \frac{\sqrt{3}}{2}$
$α = 30^{0} + \tan^{- 1} (\frac{\sqrt{3}}{2})$

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