Question

The range R of projectile is same when its maximum heights are $h_1$ and $h_2$. What is the relation between R and $h_1$ and $h_2$

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

For equal ranges body should be projected with angle $\theta$ or $({90}^{\circ }-\theta )$ from the horizontal.
And for these angles : $h_1=\frac{u^{2}si{n}^2\theta }{2g}and{h}_2=\frac{u^{2}co{s}^2\theta }{2g}$
by multiplication of both height : $h_1{h}_2=\frac{u^{2}si{n}^2\theta co{s}^2\theta }{4g^2}=\frac{1}{16}{\left(\frac{u^{2}sin2\theta }{g}\right)}^2$
$\Rightarrow 16h_1{h}_2=R^2\Rightarrow R=4\sqrt{h_1{h}_2}$