Question

How much energy was converted into thermal energy during the fall of a 47.0-kg diver who jumped to a maximum height of 13.0 meters and then fell from rest, hitting the pool at a speed of 9.23 m/s?

A) 1,930 joules
B) 2,310 joules
C) 3,990 joules
D) 4,730 joules

Answer 1

The thermal energy converted during the fall of the diver can be calculated by subtracting the kinetic energy at the moment of impact from the potential energy at the maximum height.

Step-by-step explanation:

To calculate the thermal energy converted during the fall of the diver, we need to consider the change in potential energy and the change in kinetic energy. The potential energy at the maximum height is given by mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. The kinetic energy at the moment of impact can be calculated as (1/2)mv^2, where m is the mass and v is the velocity. The thermal energy converted is the difference between the potential energy and the kinetic energy.

Using the given values, the potential energy at the maximum height is (47.0 kg)(9.8 m/s^2)(13.0 m) = 6,215.4 J. The kinetic energy at the moment of impact is (1/2)(47.0 kg)(9.23 m/s)^2 = 2,131.8 J. Therefore, the thermal energy converted is 6,215.4 J - 2,131.8 J = 4,083.6 J.

So the correct answer is C) 3,990 joules.