Question

Two particle $A$ and $B$ are projected simultaneously from a fixed point on the ground. Particle $A$ is projected on a smooth horizontal surface with speed $v$, while particle $B$ is projected in air with speed $\frac{2v}{\sqrt{3}}$. If particle $B$ hits the particle $A$, the angle of projection of $B$ with the vertical is:

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. both A and B

Answer 1

The correct option is B ${60}^{\circ }$

Let B is projected at angle $\theta$ with horizontal

For A anb B to collide there horizontal component of velocity must be equal

$v_{Bx}=v_{Ax}$

$\frac{2v}{\sqrt{3}}cos\theta =v$

$cos\theta =\frac{\sqrt{3}}{2}$

$\theta ={30}^o$

Angle with vertical direction$={90}^o-\theta$

$={60}^o$