Question

A shell is fired from a cannon with a velocity $v$ at an angle $\theta$ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal mass. One of the pieces retraces its path. Speed of the other piece immediately after the explosion is:

• A. $3v\cos \theta$
• B. $2v\cos \theta$
• C. $\frac{3}{2}v\cos \theta$
• D. $\frac{\sqrt{3}}{2}v\cos \theta$

Answer 1

The correct option is A $3v\cos \theta$

From the given information, at the highest point the velocity in the horizontal direction would be $vcos\theta$. Also, given that the piece retraces the path and velocity of the mass would be $vcos\theta$ (in exactly opp. direction) .

Let us apply the law of conservation of momentum ( Initial momentum $=$Final momentum )

$\therefore mvcos\theta =\frac{m}{2}\times v_1-\frac{m}{2}\times vcos\theta$

$3vcos\theta =v_1$

$v_1=3vcos\theta$

Speed of the other piece immediately after the explosion is $3vcos\theta$