Question

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?

Answer 1

2s

Explanation:

Answer 2

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

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.