A 960 kg rollercoaster car rides on a frictionless track. At the top of the first hill, the car has speed 3.4 m/s, and at the top of the second hill the speed is 17.7 m/s. If the first hill is 82 meters high, calculate the height of the second hill.

2155.2m

Explanation:

Given that a 960 kg rollercoaster car rides on a frictionless track. At the top of the first hill, the car has speed 3.4 m/s, and at the top of the second hill the speed is 17.7 m/s. If the first hill is 82 meters high, calculate the height of the second hill.

What is needed here is the time taken by the car and the energy used. But most importantly, the acceleration

Let's assume that the accelerations are the same. Then, using the third equation of motion

V^2 = U^2 + 2aH

Let U = 0 for the first hill

Substitutes the velocity and the height to get acceleration

3.4^2 = 2 × a × 82

164a = 11.56

a = 11.56 / 164

a = 0.07 m/s^2

For the second hill, use the same formula. In this case, U = 3.4 m/s

V^2 = U^2 + 2aH

17.7^2 = 3.4^2 + 2 × 0.07 × H

313.29 = 11.56 + 0.14H

313.29 - 11.56 = 0.14H

301.73 = 0.14H

H = 301.73/0.14

H = 2155.2 m

Therefore, the height of the second hill is 2155.2m