Question

Because of your physics background, you have been hired by an amusement park as the technical consultant for a new ride that is being developed. Patrons get into a roller coaster car that accelerates down a steep incline. On the way down, they go through an artificial “thunderstorm” that involves sprinklers. Your boss wants customers to be subjected to the “rain” for only a short amount of time (0.3 seconds). In addition, the water spraying apparatus has already been built and provides a fixed distance (0.2 meters) along the track during which the spray comes down. Your boss wants to know how far up the incline from the water sprayer the roller coaster car should start. Acceleration is 2 m/s^2. To help think about this problem, you have built a physical model of the ride. Draw a picture of the setup. How far up the incline from the water sprayer should the roller coaster car should start?

Answer 1

Solution : let us assume the minimum velocity required to pass the 0.2 metre distance in 0.3 seconds is u.

Then. S = ut + 0.5at²

So 0.2 = u ×0.3 + 2 × 0.5 ×0.3 × 0.3

U = 0.37 m/sec

Now to gain this velocity let us take the car starts with initial velocity as zero and from a distance x. Then

U² = 2ax

So x = 0.034 metres or 3.4 cm above the incline.