Question

Two balls are projected at different angles from the same place and with the same initial speed of 50 m/s. Both balls have the same range of 216 m. The difference in their times of flight is close to

• A. 14.4 s
• B. 7.8 s
• C. 3.6 m
• D. 0 s

Answer 1

The correct option is C 3.6 m

Given that:- $u=50m/s$ and $R=216m$

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

$⟹\sin 2\theta =\frac{Rg}{u^2}=\frac{216\times 10}{{50}^2}$

$⟹\sin 2\theta =0.864$

$⟹\sin 2\theta =\frac{\sqrt{3}}{2}$

$⟹2\theta ={60}^o$ and ${120}^o$

Hence, two solutions of this equation are two angles of projection.

${\theta }_1={30}^o$ and ${\theta }_2={60}^o$

Time of Flight, $T=\frac{2u\sin \theta }{g}$

Hence, $T_2-T_1=\frac{2u}{g}(\sin {\theta }_2-\sin {\theta }_1)$

$⟹T_2-T_1=\frac{2\times 50}{10}(\frac{\sqrt{3}}{2}-\frac{1}{2})$

$⟹T_2-T_1\approx 3.6s$

Hence, answer is option-(C).