Question

Two stones $A$ and $B$ are projected from the same point. $B$ is thrown $1$ second after $A$ is thrown. $A$ is projected with a velocity of $60m/s$ at an angle ${30}^{\circ }$ with the horizontal and $B$ is projected with velocity $u$ at an angle of ${45}^{\circ }$ with the horizontal. Find $u$ if both stones hit the ground at the same time. (Take $g=10m/s$)

• A. $25m/s$
• B. $25\sqrt{2}m/s$
• C. $25\sqrt{3}m/s$
• D. $\frac{25}{2}m/s$

Answer 1

The correct option is B $25\sqrt{2}m/s$

Time of flight of stone $A$
$T_A=\frac{2u_A\sin \theta }{g}=\frac{2\left(60\right)\sin {30}^{\circ }}{10}$
$=6$ seconds

For the stones to hit at the same time, time of flight of stone $B$ $\left(T_B\right)$ should be $5$ seconds
$T_B=\frac{2u\sin {\theta }_B}{g}$
$5=\frac{2u\sin {45}^{\circ }}{10}$
$⟹u=25\sqrt{2}m/s$