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 velocity of 1 with respect to 2 after time $t=0.5s$

Answer 1

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

For particle 1 : $V_1=u_1-gt$ where $t=0.5$ s

$\therefore$ $V_1=-5-10\times 0.5=-10m/s$

For particle 2 : $V_2=u_2-gt$ where $t=0.5$ s

$\therefore$ $V_2=20-10\times 0.5=15m/s$

Relative velocity of 1 w.r.t 2 after $t=0.5$ s $V_{12}=V_1-V_2=-10-15=-25m/s$