A shell of mass `2 kg` moving at a rate of `4 m//s` suddenly explodes into two equal fragments. The fragments go in directions inclined with the original line of motion with equal velocities, If the explosion imparts `48 J` of translational kinetic energy to the fragments, find the velocity and direction of each fragment.

Explanation

To solve the problem step by step, we will apply the principles of conservation of momentum and conservation of energy.

### Step 1: Understand the Problem
A shell of mass `2 kg` is moving with a velocity of `4 m/s`. It explodes into two equal fragments, each of mass `1 kg`. The explosion imparts `48 J` of kinetic energy to the fragments.

### Step 2: Conservation of Momentum
Since the shell explodes, we can use the conservation of momentum in both the x and y directions.

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