Question

How high should the engineer make the hill?

Answer 1

Answer: The height of hill is 125 feet.

Explanation:

Given that velocity of the rollercoaster is
`v= \sqrt{(v_\limit{0}^(2) )+64h}`

Where,
`v_\limit{0}` is initial velocity and h is height from top of hill.

and v is velocity at height h.

Initial Velocity
`v_\limit{0}` is 10feet/sec at top of hill.

Also, Velocity at bottom of the hill is 90feet/sec.

Therefore, the value of h at top of the hill is h=0 and value of h at bottom of the hill is h=h

`v= \sqrt{(v_\limit{0}^(2) )+64h}`

`90= \sqrt{(10)^(2) +64h}`

`90^(2)= 10^(2) +64h`

8100=100+64h

8000=64h

h=125 feets.

Thus, The height of hill is 125 feet.