this model shows a ball being shot from the cannon. which of these statements accurately describes the energy of the cannonball? select all that apply.
a the kinetic energy is lowest at point e.
b the potential energy is lowest at point e.
c the kinetic energy is greatest at point c.
d the potential energy is greatest at point c.
e the ball changes from kinetic to potential energy at point a.

Question

Accepted Answer

# Brief Explanations:
- **Option A**: Kinetic energy depends on speed. At point E, the ball is on the ground, but when it's moving (before stopping), its speed might not be lowest. At point C (highest point), vertical speed is zero (horizontal speed remains), so kinetic energy is lower there than at E (when moving). So A is incorrect.
- **Option B**: Potential energy (gravitational) depends on height ($PE = mgh$). Point E is at the lowest height (ground level), so $PE$ is lowest here. B is correct.
- **Option C**: At point C, the ball is at the highest height, so most kinetic energy has converted to potential energy (vertical speed is zero, only horizontal speed). So kinetic energy is not greatest at C. C is incorrect.
- **Option D**: Since $PE = mgh$, and point C is the highest, $PE$ is greatest here. D is correct.
- **Option E**: At point A, the ball is being shot, so it has kinetic energy (from the cannon) and starts gaining potential energy as it rises. The energy conversion is kinetic to potential (and some to heat, air resistance), but at point A, it's mostly kinetic initially, then converting. However, the statement says "changes from kinetic to potential at point A" – actually, the conversion happens as it moves from A to C. But maybe the intended idea is that at A, it has kinetic, and as it goes up, kinetic becomes potential. But more accurately, at point C, potential is max, kinetic (vertical) is min. But let's re - evaluate: At point A, the ball is launched, so it has kinetic energy. As it moves up (towards C), kinetic energy (vertical component) decreases, potential energy increases. So the conversion from kinetic to potential happens during the ascent (from A to C). But the statement "The ball changes from kinetic to potential energy at point A" – maybe it's a bit simplistic, but let's check the other options. Wait, D and B are correct. Wait, let's re - check D: Point C is the highest, so $PE = mgh$ is maximum there. Correct. B: Point E is lowest height, so $PE$ is lowest. Correct. What about E? At point A, the ball is moving (kinetic) and starts to gain potential as it goes up. But the "change" is a process, not at a single point. But maybe the question considers that at A, it's kinetic, and as it moves, it becomes potential. But let's see the other options. Let's confirm:

- Kinetic Energy (KE) and Potential Energy (PE) relationship: Total mechanical energy (ignoring air resistance) is $KE + PE = constant$. At the highest point (C), PE is maximum, so KE (vertical component) is minimum (but horizontal KE remains). At the lowest point (E, ground), PE is minimum, so KE (if moving) is maximum (but when it hits E, it might stop, but in the trajectory, before stopping, at E, it's moving horizontally? Wait, the diagram shows E on the ground. So when the ball reaches E, it's at rest? Or moving? The cannon is shooting it, so the trajectory ends at E. So at E, the ball is on the ground, so PE is minimum (h = 0). KE: when it's at C, vertical speed is 0, so KE is due to horizontal speed. At E, if it's on the ground, maybe it's stopped, but in the trajectory, as it falls from D to E, it gains KE (since PE is converting to KE). So at E, just before stopping, KE is high. At C, KE is lower (only horizontal). So A is wrong (KE is not lowest at E). B: PE is lowest at E (h = 0), correct. C: KE is greatest at C? No, because at C, PE is greatest, so KE is least (vertical component zero), so C is wrong. D: PE is greatest at C (highest point), correct. E: "The ball changes from kinetic to potential energy at point A" – at point A, the ball has kinetic energy (from being shot) and as it moves up (towards B and C), it gains potential energy (loses kinetic energy). So the conversion from kinetic to potential happens as it moves from A to C, not at point A. So E is incorrect.

So the correct options are B and D.

# Answer:
B. The potential energy is lowest at point E, D. The potential energy is greatest at point C

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