Question

Greg is in a car at the top of a roller-coaster ride. The distance, d, of the car from the ground as the car descends is determined by the equation d = 144 – 16t^2, where t is the number of seconds it takes the car to travel down to each point on the ride. For which interval of time is Greg’s car moving in the air?

Answer 1

It takes 3 seconds over the interval [0,3]

Explanation:

To find when the roller coaster reaches the ground, find when d=0.

`0=144-16t^2`

To solve divide each term by 16 and factor:

`(0)/(16)=(144)/(16) -(-16t^2)/(16)  \\0= 9 - t^2\\0=(3-t)(3+t)`

Solve for t by setting each factor to 0.

t-3=0 so t=3

t+3=0 so t=-3

This means the car is in the air from 0 to 3 second.