Question

A bomb explodes in air when it has a horizontal speed of $10m/s$. It breaks into two pieces $A$ and $B$ of mass ratio $1:2$. If $A$ goes vertically up at a speed of $40m/s$, the speed of $B$ is

• A. $20m/s$
  
• B. $50m/s$
  
• C. $30m/s$
  
• D. $25m/s$
  

Answer 1

The correct option is D $25m/s$


Draw a diagram of given situation.

Find the speed of $B$.
Formula used: $p_i=p_f$
Horizontal speed $=10m/s$
$A$ and $B$ of mass ratio $1:2$
Speed of $A=40m/sec$
By the momentum conservation in $x$ direction,
$p_i=p_f$
$3m\times 10=2mv\cos \theta$
$\Rightarrow v\cos \theta =15$
Again, the momentum conservation in 𝑦 direction,
$p_i=p_f$
$0=m\times 40+2mv\sin \theta$
$\Rightarrow v\sin \theta =-20$
Net velocity of particle $B$,
$v=\sqrt{(v\sin \theta {)}^2+(v\cos \theta {)}^2}=25m/s$
Final Answer: $\left(B\right)$