Answer:
1)

2)

Step-by-step explanation:
Given:
- mass of heavier student,

- mass of lighter student,

- velocity of the heavier student after the mutual push,

1)
Since they push each other and we are neglecting any friction that means we can consider this as a perfectly elastic collision. So the momentum of the two bodies will be equal and in opposite direction.
Since momentum is a vector quantity so the total momentum of the system as a whole will be zero.
2)
From the condition of elastic collision:



