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 masses. One of the pieces retraces its path to the cannon. The 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. $V\cos \theta$

Answer 1

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

At the top of its path, its velocity is $V\cos \theta$ only in horizontal direction, So after explosion to retrace its path velocity of one of the equal masses should be $V\cos \theta$.

Now, if we conserve the momentum then $2mV\cos \theta =mV\cos \theta +mv$

Applying conservation of momentum

$m\left(V\cos \theta \right)=\frac{m}{2}(-u\cos \theta )+\frac{m}{2}{V}_1$

Hence, we get

$V_1=3V\cos \theta$