Answer: The height of hill is 125 feet.
Step-by-step explanation:
Given that velocity of the rollercoaster is [tex]v= \sqrt{(v_\limit{0}^{2} )+64h}[/tex]
Where, [tex]v_\limit{0}[/tex] is initial velocity and h is height from top of hill.
and v is velocity at height h.
Initial Velocity [tex]v_\limit{0}[/tex] 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
[tex]v= \sqrt{(v_\limit{0}^{2} )+64h}[/tex]
[tex]90= \sqrt{(10)^{2} +64h}[/tex]
[tex]90^{2}= 10^{2} +64h[/tex]
8100=100+64h
8000=64h
h=125 feets.
Thus, The height of hill is 125 feet.
