Question

(a)
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 for sure without the measured speed or energy loss data, but here is the direct test you should use and how to interpret the result.

Claim (method): Using conservation of mechanical energy (neglecting non‑conservative losses), mgh = 1/2 m v^2, so the maximum drop height implied by a measured speed v is
h = v^2/(2g) (with g = 9.80 m/s^2).

How to use it
- Measure the coaster speed v at the lowest point after the drop.
- Compute h_calc = v^2/(2g).
- Interpretation:
- If h_calc ≈ 51 m (within experimental uncertainty), the 51 m claim is consistent with the speed measurement.
- If h_calc > 51 m, the claim is inconsistent (coaster would require more than 51 m of drop to reach that speed unless extra energy was added).
- If h_calc < 51 m, the claim could still be true because energy losses (friction, air drag, rotational energy of wheels/cars) reduce the measured speed. In that case you must estimate those losses to decide.

Two quick examples
- Example A: v = 32.0 m/s → h = v^2/(2g) = 32.0^2/(2·9.80) = 1024/19.6 = 52.2 m. This is very close to 51 m → claim plausible.
- Example B: v = 30.0 m/s → h = 30.0^2/(19.6) = 900/19.6 = 45.9 m. This is less than 51 m; that does not prove the claim false because losses could explain the lower speed — you would need to estimate work lost to friction/drag/rotation to conclude.

If you give me the measured speed (or measured kinetic energy) and any estimates of losses, I will compute h_calc and tell you whether the 51 m claim appears true.