Question

How high should the engineer make the hill?

Answer 1

Answer: The height of hill is 125 feet.

Step-by-step 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.