Question

Two balls are projected upward simultaneously with speeds $40\text{m/s}$ and $60\text{m/s}$. Relative position $\left(x\right)$ of second ball w.r.t. first ball at time $t=5\text{s}$ is :
[Neglect air resistance]

• A. $20\text{m}$
• B. $80\text{m}$
• C. $100\text{m}$
• D. $120\text{m}$

Answer 1

The correct option is C $100\text{m}$

Let the velocity of projections be $v_1$ and $v_2$.
Relative velocity of ball $2$ w.r.t $1$, $u_{rel}=v_2-v_1=60-40=20\text{m/s}$

Since, both the balls are moving under constant acceleration due to gravity. Therefore, relative acceleration of ball $2$ w.r.t ball $1$ will be zero.
$\Rightarrow a_{\text{rel}}=0$

Position of ball $2$ w.r.t ball $1$,
$s_{\text{rel}}=u_{\text{rel}}t+\frac{1}{2}{a}_{\text{rel}}{t}^2$
$\Rightarrow s_{\text{rel}}=20\times 5$
$\Rightarrow s_{\text{rel}}=100\text{m}$

Hence, option $\left(\text{C}\right)$ is the correct choice.