Problem 11.

At an amusement park there is a roller coaster ride ("ride of Steel"). After the first drop, riders are moving at the speed of 120 km/h, entering an underground tunnel. Given the fact that the roller coaster was moving at a speed of 4 km/h at the top of the hill, determine the vertical drop that these participants fell through. Neglect friction.

Solution:

In the problem we need to use energy conservation law: since the friction is zero then the mechanical energy, which is the sum of kinetic energy and gravitational potential energy, is constant.

We need to use the correct SI units, which means that the speed should be measured in m/s. Then

Now we need to write the energy conservation law. The initial mechanical energy is the sum of initial potential energy and the initial kinetic energy:

The final energy is

The initial energy is equal to the final energy. Then

From the equation we obtain

We know the initial velocity, the final velocity, the initial height (it is zero). Then we can find the final height (vertical drop):