Energy Conservation: How High Can a Bike Rider Reach Coasting Up a Hill?

Question:

If a bike rider approaches a hill at an initial velocity of 8.5 m/s and the mass of the bike and rider is 85 kg, what is the final height the rider can reach coasting up the hill?

Answer:

3.9 m

Explanation:

Assuming no energy losses, then all kinetic energy is converted to potential energy. The formula used is:

[tex]0.5mv^{2}=mgh[/tex]

Making h the subject of the formula gives:

[tex]h=\\frac {v^{2}}{2g}[/tex]

Where m is the mass of the bike rider and bike, v is the velocity, and g is acceleration due to gravity. Taking g as 9.81 m/s^2 and v as 8.5 m/s, we can calculate the height:

[tex]h=\\frac {8.5^{2}}{2\\times 9.81}=3.946992864\\approx 3.9 m[/tex]

Therefore, the bike rider can reach a final height of approximately 3.9 meters when coasting up the hill.