Question

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

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

Answer 1

Answer: (D)

$50\,m\,s^{-1}$

Answer 2

Here, $u_A = -0$ , $u_B = +50\, m\, s^{-1}$ $a_{A}=-g$ , $a_{B}=-g$ $u_{BA}=u_{B}-u_{A}=50\,m\,s^{-1}-(-0)\,m\,s^{-1}=50\,m\,s^{-1}$ $a_{BA}=a_{B}-a_{A}=-g-\left(-g\right)=0$ $\because v_{BA}=u_{BA}+a_{BA}t\quad\left(As\,a_{BA}=0\right)$ $\therefore v_{BA}=u_{BA}$ 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 $( = 50\, m\, s^{-1})$ .