Question

Two particles are projected from towers of different heights with velocities as shown in the figure. Find angle ${}^{\prime }{\theta }^{\prime }$; if the particles collide

(Given particles collide after 1 second and particles are projected at the same instant)

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

For the particles to collide
$(S_{rel}{)}_y=10$
Here upward direction is assumed to be positive and, we are talking about the motion of $A$ w.r.t $B$.
Vertical component of relative velocity of A w.r.t B, $u_{AB}=60\sin \theta -20$
Acceleration of A w.r.t B, $a_{AB}=g-g=0$, $t=1\text{s}$
Using second equation of motion,
$(S_{AB}{)}_y=(u_{AB}{)}_{y}t+\frac{1}{2}(a_{AB}{)}_y{t}^2$
$10=(60\sin \theta -20)t+0$
$10=60\sin \theta -20$
$30=60\sin \theta$
$\theta ={30}^{\circ }$