this one is easy..

The horizontal range of a projectile is 4 3 \sqrt{ 3 } times its maximum height. Its angle of projection will be .....?

90 40 30 25

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1 solution

Abhishek Singh
Mar 20, 2014

we know that horizontal range R = u 2 × sin 2 θ g . . . . . . . . . . . . . . . . . . . ( 1 ) R = \frac{u^{2} \times \sin 2\theta}{g}...................(1) and height H = u 2 × sin 2 θ 2 g . . . . . . . . . . . . . . . . . ( 2 ) H= \frac{u^{2} \times \sin^{2}\theta}{2g} .................(2) dividing ( 2 ) (2) by ( 1 ) (1) we get H R = tan θ 4 = 1 4 × 3 \frac{H}{R}=\frac{\tan\theta}{4} =\frac{1}{4 \times \sqrt{3} } which gives tan θ = 1 3 = tan 3 0 o \tan\theta= \frac{1}{\sqrt{3}}= \tan 30^{o} hence θ = 3 0 o \theta=\boxed{30^{o}}

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