Q. 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) $\sqrt{\left( u^{2} - gt \right)}$
Explanation
(a) 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 $B,\ u_{B} = 0 + gt$
$\therefore Relative\ speed,\ \mathrm{\Delta}\mathbf{v} = \mathbf{v}_{A} - \mathbf{v}_{B}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = (u - gt)\widehat{\mathbf{j}} - \left( - gt\widehat{\mathbf{j}} \right) = u\widehat{\mathbf{j}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.