A roller coaster car has a speed of v0 = 8.9 m/s as it tops the crest of a h = 26.5 m drop.

Question

What is the car's speed at the bottom of the drop, v_f in m/s? 

Answer 1

v₀ = 8.9 m/s, h₀ = 26.5 m h_final = 0 m, v_final = ? (unknown)

Assuming there is no frictional loss or external gain or loss of energy, the initial energy must equal the final energy (according to the law of conservation of energy).

E_initial = E_final

KE_initial + PE_initial = KE_final + PE_final

1/2 m v₀² + mgh₀ = 1/2 m v_f² + mgh_f

1/2 v₀² + gh₀ = 1/2 v_f² + gh_f (mass cancels out of each term)

1/2 (8.9)² + 9.8(26.5) = 1/2 v_f² + 0

24.47 = v_f