Question

Two projectiles $A$ and $B$ are thrown from the same point with velocities $v$ and $\frac{v}{2}$ respectively. If B is thrown at an angle ${45}^{\circ }$ with horizontal, what is the inclination of A with horizontal when their ranges are same?

• A. ${\text{sin}}^{-1}\left(\frac{1}{4}\right)$
• B. $\frac{1}{2}{\text{sin}}^{-1}\left(\frac{1}{4}\right)$
• C. $2{\text{sin}}^{-1}\left(\frac{1}{4}\right)$
• D. $\frac{1}{2}{\text{sin}}^{-1}\left(\frac{1}{8}\right)$

Answer 1

The correct option is B $\frac{1}{2}{\text{sin}}^{-1}\left(\frac{1}{4}\right)$

We know that range of projectile$R=\frac{v^2\text{sin}2\theta }{g}$
$R_A=R_B$
$\frac{v^2\text{sin}2\theta }{g}=\frac{{\left(\frac{v}{2}\right)}^2\text{sin}{90}^{\circ }}{g}$
$\text{sin}2\theta =\frac{1}{4}\Rightarrow 2\theta ={\sin }^{-1}\left(\frac{1}{4}\right)$
$\therefore \theta =\frac{1}{2}{\text{sin}}^{-1}\left(\frac{1}{4}\right)$