How high should the engineer make the hill?

Question

asked Jun 10, 2020 62.6k views

1 Answer

Bones · Answer 1 · 2020-06-16T23:14:32+0000

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.