Question

Trajectories of two projectiles are shown in figure. Let $T_1$ and $T_2$ be the time periods and $u_1$ and $u_2$ their speeds of projection. Then:

• A. $T_2=T_1$
• B. $T_1>T_2$
• C. $u_1>u_2$
• D. $u_1<u_2$

Answer 1

The correct option is A $T_2=T_1$

Since the height of both the projectiles are same,we have:$H_1=H_2$

$\frac{u_1^2{\sin }^2{\theta }_1}{2g}=\frac{u_2^2{\sin }^2{\theta }_2}{2g}$

$u_1^2{\sin }^2{\theta }_1=u_2^2{\sin }^2{\theta }_2$

$u_1\sin {\theta }_1=u_2\sin {\theta }_2$ wher u is initial speed and $\theta$ is the angle of projectile.

$\frac{T_1}{T_2}=\frac{\frac{2u_1\sin {\theta }_1}{g}}{\frac{2u_2\sin {\theta }_2}{g}}=\frac{2u_1\sin {\theta }_1}{g}\times \frac{g}{2u_2\sin {\theta }_2}=\frac{u_1\sin {\theta }_1}{u_2\sin {\theta }_2}=1T_1=T_2$