Question

Two particles $1$ and $2$ are thrown in the directions shown in figure simultaneously with velocities $5m/s$ and $20m/s$. Initially, particle $1$ is at height $20m$ from the ground. Taking upwards as the positive direction, find the time when the particles will collide.

Answer 1

Given : $u_1=-5m/s$ $u_2=20m/s$

Let the particles collide at point P after time $t$

For particle 1 : $S_1=u_{1}t-\frac{1}{2}g{t}^2$ where $g=10m/s^2$

$\therefore$ $-x=-5t-5t^2$ ..............(a)

For particle 2 : $S_2=u_{2}t-\frac{1}{2}g{t}^2$

$\therefore$ $20-x=20t-5t^2$ ..............(b)

Subtracting (a) from (b) we get $20=25t$ $⟹t=0.8$ s