Question

Two projectiles $A$ and $B$ are projected with velocities $\sqrt{2}v$ and $v$ respectively. They have the same range. If $A$ is thrown at angle of ${15}^o$ with the horizontal, then what is the angle of projection of $B$?

Answer 1

From formual of Range-

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

$\frac{R_1}{R_2}={\left(\frac{u_1}{u_2}\right)}^2\times \left(\frac{\sin 2x_1}{\sin 2x_2}\right)$

$\sin 2x_2=\sin 2x_1\times {\left(\frac{u_1}{u_2}\right)}^2\dots \dots [R_1=R_2]$

$\sin 2x_2=\sin 30\times {\left(\frac{\sqrt{2}v}{v}\right)}^2$

$\sin 2x_2=1$

$\sin 2x_2=\sin 90$

$x_2=\frac{90}{2}$

$x_2=45$

Angle of projection of B is ${45}^0$