Question

At Great Adventure Amusement Park in New Jersey, a popular ride known as "Free Fall" carries passengers up to a height of 33.5 m and drops them to the ground. How fast are the passengers going at the bottom on this exhilarating journey?

Answer 1

`v = 25.63`

Explanation:

Assuming that the passengers are indeed subject to free fall, we just use the kinematic equation with initial velocity zero and an acceleration of g = 9.81 m/s :

`v = v_0 + at`

Where we set `v_0 = 0` and `a=g=9.81m/s` as stated above. Now we still have one more unknown : the time t. Thats why the initial height is given, 33.5m. The time in free fall for going that distance is then :

`h = 1/2 g t^2 => t = +- sqrt(2h/g) = +2.61s` , we obviously take the positive value, for negative time has no meaning here.

Hence

`v = 25.63m/s`

Note : This question can also be solved in one line using the kinematic equation that is really the combination of the two above:
`v^2 = v_0^2 +- 2gh`, where it is plus if the acceleration adds speed to the initial one and minus if it decreases it.