Question

A bicyclist starting from rest applies a force of F = 454 N to ride his bicycle across flat ground for a distance of d = 250 m before encountering a hill making an angle of θ = 21 degrees with respect to the horizontal. The bicycle and rider have a mass of m = 136 kg combined. In this problem, you can ignore air resistance and other losses due to friction.

1. How much work, W in joules, did the rider do before reaching the hill?
2. If the cyclist starts coasting at the bottom of the hill, what distance, d, in meters, does the bike travel up the incline?

Answer 1

1.) 113500J

2.) 237m

Step-by-step explanation:

Hello!

To solve this exercise follow the following steps, the description and complete process is in the attached image

1. Draw the full sketch of the problem.

2. The work is defined as the product of the trajectory by the force that is parallel to this direction, for this reason to find the work done we multiply the horizontal distance (250m) by the applied force (454N)

3. The potential energy is equal to the product of mass, gravity and height and is equal to the work done by the force applied by the cyclist, of this relationship and using algebra we can find the height that the cyclist climbed

4. We use the sine function to find the diagonal distance using the height and angle of the slope