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?
options:
( 0lt tleq3 )
( - 3lt tleq3 )
( tgt3 )
( 0lt tlt3 )

Explanation:

Step1: Find when the car is on the ground

Set \( d = 0 \) (ground level) in \( d = 144 - 16t^2 \).
\( 0 = 144 - 16t^2 \)

Step2: Solve for \( t \)

\( 16t^2 = 144 \)
\( t^2=\frac{144}{16}=9 \)
\( t = \pm3 \)
Since time \( t\geq0 \), we consider \( t = 3 \).

Step3: Determine the interval when in the air

The car starts at \( t = 0 \) (top of the ride) and is on the ground at \( t = 3 \). So the time in the air is when \( 0 < t < 3 \) (before reaching the ground at \( t = 3 \), and \( t>0 \) as time starts at 0).

Answer:

\( 0 < t < 3 \) (the option corresponding to this interval)