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  4. Two particles are projected simultaneously from the level ground as shown in figure. They may collide after a time:

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Q. Two particles are projected simultaneously from the level ground as shown in figure. They may collide after a time:Physics Question Image

Motion in a Plane

Solution:

$x+u_2 \cos \theta_2 t=u_1 \cos \theta_1 t$
$\therefore t=\frac{x}{u_1 \cos \theta_1-u_2 \cos \theta_2} $..........(i)
$\text { Also } u_1 \sin \theta_1=u_2 \sin \theta_2$...........(ii)
After solving above equations, we get
$t=\frac{x \sin \theta_2}{u_1 \sin \left(\theta_2-\theta_1\right)}$