A bomb moving with velocity `40 hat(i)+50hat(j)+25hat(k)` m/s explodes into pieces of mass ratio 1 : 4. If the small piece goes out with velocity `200hat(i)+70 hat(j)-15hat(k)m//s`, find the velocity of larger piece after explosion.

Explanation

To solve the problem, we will apply the principle of conservation of momentum. The momentum before the explosion must equal the momentum after the explosion.

### Step 1: Determine the initial momentum of the bomb
The initial momentum \( P_i \) of the bomb can be calculated using the formula:
\[ P_i = m \cdot \vec{V} \]
where \( m \) is the mass of the bomb and \( \vec{V} \) is its velocity. Given that:
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