Final answer:
The work done by gravity as an 88.0 kg bicyclist moves 19.0 m up a 10° hill is approximately -2842.96 J. This is calculated by first finding the vertical height using the sine of the incline angle and then using the work done by gravity formula.
Step-by-step explanation:
The work done by gravity when a bicyclist moves up a hill can be calculated using the formula W = m × g × h, where m is the mass of the cyclist and the bicycle, g is the acceleration due to gravity, and h is the vertical height gained. To find h, we can use the sine function since we know the incline angle and the distance traveled along the incline.
First, let's determine the height h using the given angle θ = 10.0° and the distance s = 19.0 m:
h = s × sin(θ) = 19.0 m × sin(10.0°) ≈ 3.29 m
Now, calculating the work done by gravity Wg:
Wg = m × g × h = 88.0 kg × 9.8 m/s² × 3.29 m ≈ 2842.96 J
The work done by gravity is negative since it acts opposite to the direction of motion. Therefore, Wg ≈ -2842.96 J.