Question

A shell is fired from a cannon with a velocity V(m/s) at an angle θwith 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 to the cannon and the speed (in m/s) of the other piece immediately after the explosion is

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

Answer 1

Answer: (A)

3V cosθ

Answer 2

By the principle of conservation of momentum, mV cos

θ = $\frac{m}{2}$V cos θ + $\frac{m}{2}$V'

i.e., $\left( 1 + \frac{1}{2} \right)$ mV cos θ = $\frac{m}{2}$V'

i.e., V' = 3V cos θ