Question

a bottlenose dolphin (tursiops truncatus) is about (2.3\text{ m}) long and has a mass of (260\text{ kg}). it can jump (3.5\text{ m}) above the surface of the water while flipping nose-to-tail at (6.3\text{ rad/s}), fast enough to complete (1.5) rotations before landing in the water.

part a
how much energy must the dolphin generate to jump (3.5\text{ m}) above the surface of the water?
express your answer to two significant figures and include appropriate units.

part b
if the dolphins moment of inertia about its rotation axis is (300\text{ kg}cdot\text{m}^2), how much energy must the dolphin generate to rotate its body in this way?
express your answer to two significant figures and include appropriate units.

Explanation:

Calculate translational energy for the jump

Using the Conservation of Energy knowledge point

$$
LATEXBLOCK0
$$

Calculate rotational kinetic energy

Using the Rotational Kinetic Energy knowledge point

$$
LATEXBLOCK1
$$

Answer:

Question Part A

\(8.9 \times 10^3\text{ J}\)

Question Part B

\(6.0 \times 10^3\text{ J}\)