First slide

Projection Under uniform Acceleration

Question

The range R of projectile is same when its maximum heights are $h_{1} and h_{2}$ .What is the relation between R, $h_{1}$ and $h_{2}$ ?

Moderate

A

R = $\sqrt{h_{1} h_{2}}$
B

$R = \sqrt{2 h_{1} h_{2}}$
C

R = $2 \sqrt{h_{1} h_{2}}$
D

R = $4 \sqrt{h_{1} h_{2}}$

Solution

Range is same for angles of projection $θ and 90 - θ$
R = $\frac{u^{2} \sin 2 θ}{g}$
$h_{1} = \frac{u^{2} \sin^{2} θ}{2 g} and h_{2} = \frac{u^{2} \cos^{2} θ}{2 g}$
Hence, $\sqrt{h_{1} h_{2}} = \frac{u^{2} \sin θ \cos θ}{2 g}$
= $\frac{1}{4} [\frac{u^{2} \sin 2 θ}{g}] = \frac{R}{4}$

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