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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?

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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.

[tex]0=144-16t^2[/tex]

To solve divide each term by 16 and factor:

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

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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