Question

A 47.0-kg diver jumped to a maximum height of 13.0 meters. From there, the diver falls from rest and hits the pool at a speed of 9.23 m/s. How much energy was transferred into thermal energy during the fall?

1) 1,930 J
2) 2,310 J
3) 3,990 J
4) 4,730 J

Answer 1

The energy transferred into thermal energy during the fall is 3,990 J.

Step-by-step explanation:

First, let's calculate the potential energy at the maximum height of 13.0 meters:

Potential energy = mass x acceleration due to gravity x height

Potential energy = 47.0 kg x 9.8 m/s^2 x 13.0 m = 6,143.4 J

Next, let's calculate the kinetic energy when the diver hits the pool:

Kinetic energy = 0.5 x mass x velocity^2

Kinetic energy = 0.5 x 47.0 kg x (9.23 m/s)^2 = 2,318.6 J

To find the energy transferred into thermal energy during the fall, we subtract the initial potential energy from the final kinetic energy:

Energy transferred into thermal energy = final kinetic energy - initial potential energy

Energy transferred into thermal energy = 2,318.6 J - 6,143.4 J = -3,824.8 J

Since energy cannot be negative, we take the absolute value:

Energy transferred into thermal energy = | -3,824.8 J | = 3,824.8 J

Therefore, the correct answer is option 3) 3,990 J.