Consider the diver shown in the figure diving from a 10-m high platform. The diver completes 1.5 rotations, while also rising and falling vertically and moving forward horizontally. We will assume the diver is 1.75 m 73 kg diver. In this problem, we will consider only the in-plane motion of the diver’s center of mass. In dynamics problems we can usually break motion into linear and rotational motion and solve for each component separately.

A) If the diver spends 2.0 seconds in the air and enters the water 4.0 m horizontally from their takeoff point on the platform, calculate takeoff velocity and angle.

B) Consider the diver’s rotational motion. Assume that at launch the diver throws their arms up and forward so that they are fully stretched and rotates at p radians per second, enough to complete one full rotation in the 2.0 seconds that they are in the air. Use the moment of inertia formulas shown below to calculate how much their rotational velocity increases when they tuck into a ball for they somersault and how much their rotational velocity decreases again when they fully stretch out again prior to entry. Assume that the diver is shaped like a cylinder rotating about a short axis (x in Fig. b) when stretched and like a disk rotating about its central axis ( z in Fig. b) when tucked. Will they be able to complete 1.5 rotations before entering the water? Explain all assumptions, including how you came up with the dimensions you used 

Transcribed Image Text:

Ixx = Izz = 1 1 my 2 12m (3r + h) V = rh h Z (a) The swim dive Y (b) Cylinder-like motion rotational Ixx = Izz = 1 1 my 2 12m (3r + h) V = rh h Z (a) The swim dive Y (b) Cylinder-like motion rotational