Assertion: A rocket launched vertically upward explodes at the highest point it reaches. the explosions produces three fragments with non-zero initial velocity. Then, the initial velocity vectors of all the three fragments are in one plane.
Reason For sum of momentum of three particles, all the three momentum vectors must be coplanar.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the problem, we need to analyze the assertion and the reason provided in the question regarding the explosion of a rocket and the behavior of its fragments.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that when a rocket is launched vertically upward and explodes at its highest point, it produces three fragments with non-zero initial velocities. It claims that the initial velocity vectors of all three fragments are in one plane.

2. **Analyzing the Situation**:
- When the rocket reaches its highest point, its vertical velocity becomes zero. At this point, if it explodes, the fragments will have some initial velocities but they will still be influenced by the conditions at that moment (i.e., the vertical motion has ceased).

3. **Momentum Conservation**:
- According to the law of conservation of momentum, the total momentum before the explosion must equal the total momentum after the explosion.
- Since the rocket is at the highest point, its momentum in the vertical direction is zero. Therefore, the vector sum of the momenta of the fragments must also be zero.

4. **Implication of Coplanarity**:
- For the total momentum to be zero, the momentum vectors of the fragments must be arranged such that they cancel each other out. This is only possible if the momentum vectors are coplanar (i.e., they lie in the same plane).
- If the fragments have non-zero initial velocities, their momentum vectors must also be in the same plane to satisfy the condition of zero total momentum.

5. **Conclusion**:
- Thus, the assertion is true: the initial velocity vectors of all three fragments are indeed in one plane.
- The reason is also true: for the sum of the momenta of the three fragments to be zero, their momentum vectors must be coplanar.

6. **Final Answer**:
- Both the assertion and the reason are true, and the reason correctly explains the assertion.