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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 – 16t2, 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?

Verified Answer :

MrsStrong

Answer:

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

Step-by-step 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:

\(\frac{0}{16}=\frac{144}{16} -\frac{-16t^2}{16}  \\0= 9 - t^2\\0=(3-t)(3+t)\)

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.

The time interval will be 0<t<3  or (0, 3)

What is interval?

A interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

Given:

d = 144 – 16t²

Now,

d>0

144 – 16t²>0

144>16t²

144/16>t²

9>t²

t<±3

Since, time can't be negative.

So, t<3

Hence, the interval for which Greg’s car moving in the air is,  0<t<3  or (0, 3).

Learn more about this concept here:

https://brainly.com/question/2055227

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