Question

a bicyclist is stopped at the entrance to a valley, as sketched below:

where would the bicyclist have the highest potential energy? select
where would the bicyclist have the lowest potential energy? select
where would the bicyclist have the highest kinetic energy? select
where would the bicyclist have the highest speed? select
would the bicyclist’s kinetic energy be higher at c or a? select
would the bicyclist’s potential energy be higher at c or a? select
would the bicyclist’s total energy be higher at c or a? select
suppose the bicyclist lets off the brakes and coasts down into the valley without pedaling. even if there is no friction or air resistance to slow him down, what is the farthest point the bicyclist could reach without pedaling? select

Explanation:

Potential energy (PE) depends on height: $PE = mgh$ (higher height = higher PE). Kinetic energy (KE) depends on speed: $KE = \frac{1}{2}mv^2$; without friction, PE converts to KE and vice versa (total energy conserved). Speed is proportional to $\sqrt{KE}$.

Answer:

• Highest potential energy: Point A (highest height)
• Lowest potential energy: Point C (lowest height)
• Highest kinetic energy: Point C (max PE converted to KE)
• Highest speed: Point C (highest KE)
• Kinetic energy higher at C or A? C
• Potential energy higher at C or A? A
• Total energy higher at C or A? Same (energy conserved)
• Farthest point without pedaling: Point A (same height as start, energy conserved)