Question

Does Universal Studio’s claim about the coaster’s height (51 m) appear to be true? Answer the question with a claim using your knowledge of Conservation of Energy and support it with evidence and reasoning using data and calculations.

Answer 1

I can’t decide yes/no without the measured speed or energy loss data, but here’s a short, testable claim plus the evidence and calculations you should use.

Claim (how you should evaluate it): If the car’s measured speed at the bottom of the drop is about 31.6 m/s (± a little), the 51 m claim is plausible. If the measured speed is substantially greater than 31.6 m/s the 51 m claim is not possible by gravity alone. If the measured speed is substantially less than 31.6 m/s the claim could still be true because of energy losses (friction, air drag, brakes).

Reasoning and calculations using Conservation of Energy
- Conservation of mechanical energy (ignoring non‑conservative losses) gives m g h = 1/2 m v^2, so h = v^2/(2 g).
- For h = 51 m, the maximum speed (gravity → kinetic) is
v = sqrt(2 g h) = sqrt(2 × 9.8 m/s^2 × 51 m) ≈ 31.6 m/s ≈ 114 km/h.
- Therefore:
- If you measure v ≈ 31.6 m/s at the bottom, that is consistent with a 51 m vertical drop (neglecting losses).
- If you measure v > 31.6 m/s, gravity from 51 m alone cannot have produced that speed (unless there is additional propulsion), so the 51 m claim would be false.
- If you measure v < 31.6 m/s, the ride could still be 51 m tall but have energy losses; you cannot disprove the height from a low speed alone.

How to get the needed data (practical measurement)
- Measure the coaster’s speed at the bottom of the drop (video with known frame rate + reference length on track, a GPS/phone sensor, or timing between two fixed points).
- Compute h_measured = v^2/(2 g). This gives the minimum height needed to produce the measured speed if no energy is lost. Compare h_measured to 51 m.

Example
- Suppose you measure v = 28.0 m/s. Then h = 28.0^2/(2×9.8) = 784/19.6 ≈ 40.0 m. That means 40 m of drop would be enough to produce that speed without losses — since 40 m < 51 m, the 51 m claim might still be true (the 11 m difference could be lost to friction/drag). You cannot rule out 51 m from this measurement alone.
- Suppose you measure v = 35.0 m/s. Then h = 35^2/(19.6) = 1225/19.6 ≈ 62.5 m. That exceeds 51 m, so gravity from 51 m cannot produce 35 m/s — the 51 m claim would appear false unless there is extra propulsion.

If you give me the measured speed at the bottom (or timing/video data I can use to compute it), I will do the numeric test and state whether the 51 m claim is supported or contradicted.