Question

using kinetic energy to determine height
read the scenario and solve these two problems.
when traveling at top speed, a roller coaster train with a mass of 12,000 kg has a velocity of 30 m/s. the kinetic energy of the train at top speed is 5,400,000 j.
given this kinetic energy, what is the tallest hill this roller coaster train can reach the top of?
the train can climb a hill that is blank m high.
options: 46, 92, 450, 900

Explanation:

Step1: Recall energy conservation

At the top of the hill, kinetic energy converts to gravitational potential energy: \( KE = PE = mgh \).

Step2: Solve for height \( h \)

Rearrange formula: \( h=\frac{KE}{mg} \).
Given \( KE = 5400000 \, \text{J} \), \( m = 12000 \, \text{kg} \), \( g = 9.8 \, \text{m/s}^2 \).
Substitute values: \( h=\frac{5400000}{12000\times9.8} \approx \frac{5400000}{117600} \approx 45.9 \approx 46 \).

Answer:

46