A playground slide is 8.80 ft long and makes an angle of 25.0° with the horizontal. A 63.0-kg child, initially at the top, slides all the way down to the bottom of the slide. Choosing the bottom of the slide as the reference configuration, what is the system's potential energy when the child is at the top and at the bottom of the slide? What is the change in potential energy as the child slides from the top to the bottom of the slide? (Include the sign of the value in your answer.)

Step-by-step explanation:

First, use trig to find the height of the slide.

The slide forms a right triangle. We know the hypotenuse is 8.80 ft, and the angle opposite of the height is 25.0°. So using sine:

sin 25.0° = h / 8.80

h = 3.72 ft

Converting to meters:

h = 3.72 ft * (1 m / 3.28 ft)

h = 1.13 m

Potential gravitational energy is:

PE = mgh

where m is the mass, g is the acceleration due to gravity, and h is the relative height.

At the bottom of the slide, h = 0:

PE = (63.0 kg) (9.8 m/s²) (0 m)

PE = 0 J

At the top of the slide, h = 1.13 m:

PE = (63.0 kg) (9.8 m/s²) (1.13 m)

PE = 700 J

The change is the final potential energy minus the initial potential energy.

ΔPE = 0 J - 700 J

ΔPE = - 700 J