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 $h_2?$

• A. $R=\sqrt{h_1{h}_2}$
• B. $R=\sqrt{2h_1{h}_2}$
• C. $R=2\sqrt{h_1{h}_2}$
• D. $R=4\sqrt{h_1{h}_2}$

Answer 1

Answer: (D)

Range is same for angles of projection so $\theta =90-\theta$

$R=\frac{u^{2}sin2\theta }{g}$

$h_1=\frac{u^{2}si{n}^2\theta }{2g}$ and $h_2=\frac{u^{2}co{s}^2\theta }{2g}$

Hence, $\sqrt{h_1{h}_2}=\frac{u^{2}sin\theta cos\theta }{2g}$

$=\frac{1}{4}[\frac{u^{2}si{n}^{2}2\theta }{g}]=\frac{R}{4}$