Question

A projectile can have the same range $R$ for two angles of projection. If $t_1$ and $t_2$ be the times of flight in the two cases:

• A. $t_1{t}_2\propto R^2$
• B. $t_1{t}_2\propto R$
• C. $t_1{t}_2\propto \frac{1}{R}$
• D. $t_1{t}_2\propto \frac{1}{R^2}$

Answer 1

Answer: (B)

$t_1{t}_2\propto R$

$R=\frac{v^{2}sin2{\theta }_1}{g}=\frac{v^{2}sin2{\theta }_2}{g}$

$t_1=\frac{2vsin{\theta }_1}{g}$ $t_2=2\frac{vsin{\theta }_2}{g}$

assume if ${\theta }_1=\frac{\pi }{2}-{\theta }_2$

then $t_2{t}_2=\frac{4v^{2}sin{\theta }_{1}sin(\frac{\pi }{2}-{\theta }_1)}{g^2}=\frac{2v^2\times 2sin{\theta }_{1}cos{\theta }_1}{g^2}=\frac{2}{g}\frac{v^{2}sin2{\theta }_1}{g}=\frac{2}{g}R$