Question

A shell is fired from a cannon with a velocity V at an angle θ 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 θ
(b) 2V cos θ
(c) 32 V cos θ
(d) V cos θ

Answer 1

Answer:

(a)

Explanation:

At the highest point,the velocity of the particle becomes vcosθ.Let the mass of the particle be originally '2m'.

Now it splits to 'm' and 'm'.One particle retraces the path to the cannon.This means that it goes back with velocity -vcosθ.

Let velocity of other piece be V.

According to linear momentum conservation :

2mvcosθ = -mvcosθ + mV

⇒ mV = 3 mvcosθ

⇒ V = 3vcosθ