Question

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 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 m high.

Explanation:

Step1: Calculate kinetic energy

The formula for kinetic energy is \(K.E.=\frac{1}{2}mv^{2}\).
Substitute \(m = 12000\space kg\) and \(v=30\space m/s\) into the formula:
\(K.E.=\frac{1}{2}\times12000\times30^{2}\)
\(=\frac{1}{2}\times12000\times900\)
\(=6000\times900\)
\(= 5400000\space J\)

Step2: Calculate the height of the hill

Assume all kinetic energy is converted to potential energy (\(P.E. = mgh\)).
We know \(P.E.=K.E. = 5400000\space J\), \(m = 12000\space kg\) and \(g = 9.8\space m/s^{2}\)
From \(h=\frac{P.E.}{mg}\)
\(h=\frac{5400000}{12000\times9.8}\)
\(h=\frac{5400000}{117600}\approx45.92\space m\)

Answer:

The kinetic energy of the train at top - speed is \(5400000\space J\). The tallest hill the roller - coaster train can reach the top of is approximately \(45.92\space m\) high.