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.

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Accepted Answer

# Brief Explanations:
- **Option A**: Kinetic energy depends on speed. At point E, the ball is at the lowest height (on the ground) and likely moving with significant speed (as it's falling and then moving horizontally? Wait, no—when it hits the ground at E, maybe it's still moving, but actually, potential energy (PE) is $ mgh $ (mass × gravity × height) and kinetic energy (KE) is $ \frac{1}{2}mv^2 $. At the highest point (C), KE is lowest (since speed is lowest there, as vertical speed is zero, horizontal speed remains), and PE is highest. At E (lowest height), PE is lowest. Let's analyze each:
  - **A**: At E, the ball is on the ground (lowest height). But when moving, KE is related to speed. Wait, when the ball is shot, it has KE. As it rises (A to C), KE converts to PE. At C (highest point), vertical speed is 0, so KE is minimum (but not zero, since horizontal speed exists). Then, as it falls (C to E), PE converts back to KE. So at E, which is the lowest point (same height as A? Wait, A is the cannon's height, E is ground? Wait, the cannon is on the ground? Wait, the diagram: A is the cannonball just shot, B is rising, C is the peak, D is falling, E is on the ground. So height at E is lowest (h=0, assuming ground is h=0). So PE at E is $ mgh = 0 $ (lowest). KE at E: when it hits the ground, it's moving, so KE is high. So A is wrong.
  - **B**: PE is $ mgh $. At E, height $ h $ is lowest (ground level), so PE is lowest. Correct.
  - **C**: At C (peak), vertical speed is 0, so KE is minimum (since KE depends on speed; horizontal speed is constant, but vertical speed is zero, so total speed is horizontal speed, which is less than at A or E). So KE is not greatest at C. Wrong.
  - **D**: PE is $ mgh $. At C, height $ h $ is greatest, so PE is greatest. Correct.
  - **E**: At point A, the ball is moving (has KE) and is rising (gaining PE). So energy is converting from KE to PE as it moves from A to C. So at A, the process of converting KE to PE is happening, but the statement says "changes from kinetic to potential energy at point A"—energy conversion is a process, not a single point. But more accurately, as the ball rises (from A to C), KE decreases and PE increases. So the conversion is from KE to PE during the ascent (including A). But is the statement accurate? Wait, maybe the key is: at A, the ball is moving (KE) and starting to rise (so PE increases). But the statement says "changes from kinetic to potential energy at point A"—maybe it's phrased as the point where the conversion happens, but actually, the conversion is continuous. However, let's recheck: when the ball is shot (A), it has KE. As it goes up (A to C), KE is converted to PE. So at A, the energy is mostly KE, and as it moves up, KE decreases, PE increases. So the statement "The ball changes from kinetic to potential energy at point A"—maybe it's intended to say that at A, the conversion starts. But let's check the other options first. B and D are correct? Wait, wait:
Wait, let's re-express:

- **Potential Energy (PE)**: Depends on height ($ PE = mgh $). Higher height → higher PE. So highest PE at C (highest point), lowest PE at E (lowest point, ground). So B (PE lowest at E) and D (PE greatest at C) are correct.

- **Kinetic Energy (KE)**: Depends on speed ($ KE = \frac{1}{2}mv^2 $). When the ball is shot (A), it has high KE. As it rises (A to C), speed decreases (vertical component slows down, horizontal component constant), so KE decreases (minimum at C, since vertical speed is 0, so total speed is horizontal speed). Then, as it falls (C to E), speed increases (vertical component increases downward), so KE increases (maximum at E, just before hitting the ground? Wait, E is on the ground. If E is the landing point, then at E, the ball's speed is high (since it's fallen from C, converting PE to KE). So KE at E is high, at C is low. So A (KE lowest at E) is wrong, C (KE greatest at C) is wrong.

- **Option E**: "The ball changes from kinetic to potential energy at point A"—energy conversion is a process, not a single point. As the ball moves from A to C, KE is converted to PE. So at A, the ball has KE and is starting to gain PE, but the "change" is a continuous process, not a point event. So E is not accurate.

So correct options are B and D. Wait, but let's confirm:

- B: PE is lowest at E (since h is lowest) → correct.

- D: PE is greatest at C (h is greatest) → correct.

Wait, but maybe I made a mistake with E. Let's see: when the ball is at A, it's moving (KE) and ascending (so PE is increasing, KE is decreasing). So the energy is changing from KE to PE as it moves from A to C. So the statement "changes from kinetic to potential energy at point A"—maybe it's meant to say that at A, the conversion starts, but technically, energy conversion is continuous. However, maybe the question considers that at A, the ball is moving (KE) and begins to gain PE, so the conversion happens there. But let's check the other options again.

Wait, maybe the cannon is on the ground, so A is at ground level? Wait, the diagram: A is the cannonball just after being shot, B is higher, C is peak, D is lower, E is on the ground. So A is at the same height as E? No, the cannon is on the ground, so A is at ground level, E is also at ground level? Wait, that can't be. Wait, maybe the cannon is elevated? No, the diagram shows the cannon on the ground, so A is at ground level, E is also at ground level. Then PE at A and E is the same (h=0). Then PE at C is highest. Then KE: at A, the ball is shot, so high KE. As it rises to C, KE decreases (PE increases). As it falls to E, KE increases (PE decreases). So at C, KE is lowest (vertical speed 0, horizontal speed constant). At E, KE is equal to at A (if no air resistance, conservation of energy: PE at A is 0, KE at A is $ KE_A $; PE at C is $ PE_C $, KE at C is $ KE_C = KE_A - PE_C $; PE at E is 0, so KE at E is $ KE_A $ (same as A). So KE at E is same as A, which is high. So A (KE lowest at E) is wrong. C (KE greatest at C) is wrong (KE is lowest at C). B: PE at E is 0 (lowest, since h=0), correct. D: PE at C is highest (highest h), correct. E: "changes from kinetic to potential energy at point A"—when moving from A to C, KE converts to PE. So at A, the ball has KE and starts to gain PE, so the conversion is happening. But is the statement accurate? Maybe the question considers that at A, the energy is kinetic and begins to become potential, so E is correct? Wait, no—energy conversion is a process, not a point. But maybe the question's wording is simplified. Wait, let's check the options again:

- A: KE lowest at E → E is at ground, KE at E is same as A (if no air resistance), so not lowest. Wrong.

- B: PE lowest at E → E is ground, h=0, PE=0 (lowest). Correct.

- C: KE greatest at C → C is peak, KE is lowest (vertical speed 0). Wrong.

- D: PE greatest at C → C is peak, h highest, PE highest. Correct.

- E: "The ball changes from kinetic to potential energy at point A"—when the ball is at A, it's moving (KE) and ascending (so PE increases, KE decreases). So the energy is converting from KE to PE as it moves from A to C. So the "change" is a process, but the statement says "at point A"—maybe it's intended to say that at A, the conversion starts, but technically, it's a continuous process. However, maybe the question considers that at A, the ball is moving (KE) and begins to gain PE, so E is correct? Wait, no—if A is at ground level, PE at A is 0, KE at A is high. As it moves up, PE increases (so KE decreases). So the conversion is from KE to PE during the ascent (A to C). So the statement "changes from kinetic to potential energy at point A"—maybe it's a simplification, but is it accurate? Maybe not, because the conversion is over the entire ascent, not just at A. So E is incorrect.

Thus, 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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