Final answer:
The angle θ upon release can be found using conservation of energy, the tension just before release equals the student's weight, and the maximum tension occurs at the lowest point of the swing including centripetal force.
Step-by-step explanation:
To address the student's queries:
- Angle θ when he releases the rope: Just before release, the velocity is zero, indicating that all the kinetic energy has converted into potential energy. Since the student swings out over a lake, we can presume a pendulum-like motion. At the point of release, the height of the student will be at a maximum, and we can use the conservation of energy to find the height h using the equation mgh = (1/2)mv². From this height, we can use the triangle formed by the rope and its vertical and horizontal components to find the angle θ.
- Tension in the rope just before release: At the moment just before release, when velocity is zero and the student is at the highest point of swing, the only forces acting are the tension in the rope and the student's weight. Since the student is momentarily stationary just before release, the tension in the rope equals the weight of the student (T = mg).
- Maximum tension in the rope during the swing: For the maximum tension, we must consider the lowest point in the swing where the centripetal force is at its maximum. The tension is the sum of the force providing centripetal acceleration and the weight of the student. It can be found using the equation T = mg + mv²/r, where r is the radius of the circular path which corresponds to the length of the rope.