Question

A ball A is dropped from a building of height $45m$ . Simultaneously another identical ball $B$ is thrown up with a speed $50m{s}^{-1}$ . The relative speed of ball $B$ w.r.t. ball A at any instant of time is (Take $g=10m{s}^{-2})$

• A. $0$
• B. $10m{s}^{-1}$
• C. $25m{s}^{-1}$
• D. $50m{s}^{-1}$

Answer 1

Answer: (D)

Here, $u_A=-0$ , $u_B=+50m{s}^{-1}$

$a_A=-g$ , $a_B=-g$
$u_{BA}=u_B-u_A=50m{s}^{-1}-(-0)m{s}^{-1}=50m{s}^{-1}$
$a_{BA}=a_B-a_A=-g-\left(-g\right)=0$
$\because v_{BA}=u_{BA}+a_{BA}t\left(As{a}_{BA}=0\right)$
$\therefore v_{BA}=u_{BA}$
As there is no acceleration of ball $B$ w.r.t to ball $A$ , therefore the relative speed of ball $B$ w.r.t ball $A$ at any instant of time remains constant $(=50m{s}^{-1})$ .