Final answer:
The work done by gravity is 2843.78 J and the work done by the person is 15995.58 J.
Step-by-step explanation:
To calculate the work done by gravity, we need to find the vertical component of the weight force. The weight force is given by the formula:
Weight = Mass x Gravity
W = m * g
where m is the mass of the rider and the bike, and g is the acceleration due to gravity.
In this case, m = 88.0 kg
g = 9.8 m/s^2
Therefore, the weight force is:
Weight = 88.0 kg * 9.8 m/s^2 = 862.4 N
The vertical component of the weight force is given by:
Vertical component = Weight * sin(angle)
Angle = 10.0 degrees
Vertical component = 862.4 N * sin(10.0 degrees) = 149.62 N
Therefore, the work done by gravity is the product of the vertical component of the weight force and the distance moved up the hill:
Work done by gravity = Force * Distance = 149.62 N * 19.0 m = 2843.78 J
To calculate the work done by the person, we need to find the force exerted by the person. The force exerted by the person is equal to the force of gravity parallel to the hill:
Force exerted by the person = Weight * cos(angle)
Force exerted by the person = 862.4 N * cos(10.0 degrees) = 841.82 N
Therefore, the work done by the person is the product of the force exerted by the person and the distance moved up the hill:
Work done by the person = Force * Distance = 841.82 N * 19.0 m = 15995.58 J