Question

A ball $A$ is thrown up vertically with a speed $u$ and at the same instant another ball $B$ is released from a height $h$. At time $t$, the speed of $A$ relative to $B$ is

• A. $u$
• B. $2u$
• C. $u-gt$
• D. $\sqrt{({{u}^{2}}-gt)}$

Answer 1

Answer: (A)

$u$

Answer 2

From equation of motion,
we have $v=u+gt$
where u is initial velocity and t is time.
For ball A, ${{v}_{A}}=u-gt$
For ball B, ${{v}_{B}}=0+gt$
$\therefore$ Relative speed, $\Delta \overrightarrow{v}={{\overrightarrow{v}}_{A}}-{{\overrightarrow{v}}_{B}}$
$=(u-gt)\hat{j}-(-gt\,\hat{j})$
$=u\hat{j}$