Question

(a)
According to Universal Studios, the roller coaster’s maximum height at the first hill is 51m. The mass of the roller coaster with riders is approximately 2250 kg. You are to use your knowledge of Physics to determine if this claim is true. Use the data below and answer the following questions.




figure_2_coaster_834bf396-11d3-4764-962d-6deadf97047b



Calculate the total kinetic energy of the coaster at point B. Choose the correct answer below.

A
2,025,000 J

B
67,500 J

C
1,012,500 J

D
4,050,000 J

(b)
Using your knowledge of potential and kinetic energy and the conservation of energy, calculate the height of the coaster at point A.

A
91 m

B
46 m

C
51 m

D
22 m

Answer 1

(a) C — 1,012,500 J.

Work: KE_B = 1/2 m v^2. From the figure v_B = 30.0 m/s, so
KE_B = 0.5(2250 kg)(30.0 m/s)^2 = 1,012,500 J.

(b) A — 91 m.

Use conservation of energy (neglecting friction): m g h_A = m g h_B + KE_B, so
h_A = h_B + KE_B/(m g).
From the figure h_B = 46 m, so
h_A = 46 m + 1,012,500 J / (2250 kg · 9.8 m/s^2) ≈ 46 + 45.9 ≈ 91 m (to the closest choice).

Conclusion: the claimed 51 m is not correct — the calculated height is about 91 m.