Given:
- Mass of the body (m) = 1 kg
- Mass ratio of the fragments = 1:1:3
- Speed of the two equal mass fragments (v) = 30 m/s

To Find:
- Velocity of the heavier fragment

Explanation:
The given problem can be solved using the principle of conservation of momentum and the principle of conservation of energy.

Conservation of Momentum:
- Before the explosion, the body is at rest, so the initial momentum is zero.
- After the explosion, the three fragments move in different directions with different speeds.
- According to the principle of conservation of momentum, the total momentum before and after the explosion must be the same.

Conservation of Energy:
- Before the explosion, the body has zero kinetic energy.
- After the explosion, the three fragments have kinetic energy due to their motion.
- According to the principle of conservation of energy, the total energy before and after the explosion must be the same.

Step 1: Mass Calculation
Let the masses of the three fragments be m1, m2, and m3, respectively.
Given that the mass ratio is 1:1:3, we can write:
m1 = m2 = x (let)
m3 = 3x

The total mass of the body (m) is given as 1 kg.
So, m1 + m2 + m3 = x + x + 3x = 5x = 1 kg
=> x = 1/5 kg

Therefore, m1 = m2 = 1/5 kg
and m3 = 3/5 kg

Step 2: Momentum Calculation
Before the explosion, the total momentum is zero.
After the explosion, the fragments move in different directions with different speeds.
Let the velocity of the heavier fragment (m3) be v3.

Using the principle of conservation of momentum:
(m1 * v1) + (m2 * v2) + (m3 * v3) = 0

Given that m1 = m2 = 1/5 kg and v1 = v2 = 30 m/s
(1/5 * 30) + (1/5 * 30) + (3/5 * v3) = 0
(2/5 * 30) + (3/5 * v3) = 0
(6/5) + (3/5 * v3) = 0
3/5 * v3 = -6/5
v3 = -6/5 * (5/3)
v3 = -6/3 = -2 m/s

Therefore, the velocity of the heavier fragment is -2 m/s.

Explanation:
The negative sign in the result indicates that the heavier fragment is moving in the opposite direction to the lighter fragments. This means that the heavier fragment is moving in the direction opposite to the initial motion of the body before the explosion.

Conclusion:
The velocity of the heavier fragment is -2 m/s.