Question

a bicyclist is stopped at the entrance to a valley, as sketched below; image of a graph with points a, b, c, d, l, f and a bicyclist at a where would the bicyclist have the highest potential energy? f (selected) 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 d or c? select would the bicyclist’s potential energy be higher at d or c? select would the bicyclist’s total energy be higher at d or c? 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:

Step1: Recall potential energy formula

Gravitational potential energy is $PE = mgh$, so higher height means higher PE. Point F is the highest.

Step2: Identify lowest height for min PE

Lowest height is point D, so min PE at D.

Step3: Relate KE to PE (conservation)

Without friction, $KE + PE = constant$. Lowest PE (D) means highest KE.

Step4: Link speed to KE

$KE = \frac{1}{2}mv^2$, so highest KE (D) means highest speed.

Step5: Compare D vs C height for KE

D is lower than C, so PE at D < PE at C → KE at D > KE at C.

Step6: Compare D vs C height for PE

C is higher than D, so PE at C > PE at D.

Step7: Total energy conservation

No friction → total energy (KE+PE) is constant at D and C.

Step8: Max reach without pedaling

Total energy limits height to initial height (A). The highest point ≤ A’s height is F? No—wait, initial position is A (stopped, KE=0, PE=mgh_A). Without pedaling, max height can’t exceed A’s height. If F is higher than A, no—wait, the graph: A is the starting point. The farthest point with height ≤ A’s height is the highest point equal to A’s height. Assuming F is not higher than A? Wait, initial PE is at A. So max reach is the point with same height as A (conservation of energy, no pedaling).

Answer:

1. Highest potential energy: F
2. Lowest potential energy: D
3. Highest kinetic energy: D
4. Highest speed: D
5. Kinetic energy higher at: D
6. Potential energy higher at: C
7. Total energy: Same at D and C
8. Farthest point: The point with the same height as A (assuming the highest point reachable without pedaling is the one equal to A's initial height)

Wait, correcting step8: Since the cyclist starts at A (stopped, so KE=0, total energy=PE_A=mgh_A). Without pedaling/friction, total energy remains mgh_A. So the farthest point is the highest point with height ≤ h_A. If the graph shows a point equal to A's height, that's the max. If F is higher than A, can't reach. Assuming the highest reachable is the point at A's height. But based on typical problems, if A is the start, the max reach is the point with same height as A.

Final answers (matching typical problem logic):

1. F
2. D
3. D
4. D
5. D
6. C
7. Same
8. The point with the same height as A (or if labeled, e.g., if there's a point equal to A, that's it; but based on common setups, it's the highest point not exceeding A's height)

But to align with standard physics problems for this setup: