A diver springs upward from a diving board. At the instant she contacts the water, her speed is 8.70 m/s, and her body is extended at an angle of 81.0°

initial-velocity
negative-direction

#1

A diver springs upward from a diving board. At the instant she contacts the water, her speed is 8.70 m/s, and her body is extended at an angle of 81.0° with respect to the horizontal surface of the water. At this instant her vertical displacement is −3.00 m, where downward is the negative direction. Determine her initial velocity, both magnitude and direction.

Answer:

For the sake of completeness, let us discuss and keep aside the rotational
motion of the diver.

If we remove air from the scenario and the diver being a system left to itself, whatever initial angular momentum the diver has should have been provided by the torque generated on the spring board.
During the dive, she can only alter the angular velocity by changing the moment of inertia such that the angular momentum remains a constant.

Assuming her body being stretched(extended) on contacting water, the displacement of her center of mass is equivalent to the displacement of the corresponding uppermost(or lowermost) parts of the body, whatever be the orientation.

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