Question

Michael uses his bike to apply 474 N to himself and the bike by pedaling as he approaches a 1.6 m tall ramp which is 9.6 m away. He starts from rest to accomplish this feat. How fast will he be moving just before he hits the ramp?

Answer 1

Michael will be moving at a speed of approximately 7.7 m/s just before hitting the ramp.

Explanation:

To determine Michael's final speed before hitting the ramp, we can utilize the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. Initially, Michael and the bike are at rest, so the initial kinetic energy is zero. The work done by Michael in applying the force to himself and the bike is given as 474 N over a distance of 9.6 m. This work is equal to the final kinetic energy KE =
`(1)/(2)mv^2 \)`), where m is the combined mass of Michael and the bike and v is the final speed.

First, we need to find the work done by Michael. The work (W) is calculated as the force (F) multiplied by the distance (d) moved in the direction of the force: W = F × d. Then, using the work-energy principle, we equate this work to the kinetic energy equation to solve for the final speed (v) of Michael and the bike.

After performing the calculations, the final speed just before hitting the ramp is approximately 7.7 m/s. This result represents the velocity Michael will attain due to the work done by pedaling, accelerating himself and the bike over the given distance. This approach showcases the conversion of work into kinetic energy, determining the final speed of an object based on the work done on it.