Q. A shell is fired from a cannon with a velocity $v$ at angle $\theta$ with horizontal. At the highest point, it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon. The speed of the other piece just after explosion is
A) $3\ v\cos\theta$
B) $2\ v\cos\theta$
C) $\frac{3}{2}v\cos\theta$
D) $\frac{\sqrt{3}}{2}v\cos\theta$
Explanation
(a) According to law of conservation of linear momentum at the highest point.
$mv\cos\theta = \frac{m}{2}\left( - v\cos\theta \right) + \frac{m}{2}v_{1}$
or $v_{1} = 3v\cos\theta$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.