A rollercoaster ride reaches a height of 80 feet before it sharply drops. The height above the ground of the rollercoaster car during the drop is modeled by the function, h (t) = 10t2-40t+80, where t is measured in seconds since the car started its decline. The model is accurate for 0≤t≤4. On this portion of the ride, how long does the car take to reach a minimum height from the ground before rising again?

Therefore the car takes 2 s to reach a minimum height from the ground before rising again.

Step-by-step explanation:

Given that a roller coaster ride reach a height of 80 feet.

The height above the ground of the roller coaster is modeled by the function

h (t) = 10t²-40t+80

where t is measured in second.

h (t) = 10t²-40t+80

Differentiating with respect to t

h' (t) = 10 (2t) - 40

⇒h' (t) = 20t-40

To find the minimum height we set h' (t) = 0

∴20t-40=0

⇒20t = 40

⇒t=2

The height of the roller coaster minimum when t=2 s.

The minimum height of of the roller coaster is

h (2) = 10 (2) ²-40.2+80

=40-80+80

=40 feet.

Therefore the car takes 2 s to reach a minimum height from the ground before rising again.