Question

The velocity of v in feet per second of a roller coaster at the bottom of a hill is related to the vertical drop h in feet and the velocity v° in feet per second of the coaster at the top of the hill by the formula v°=$\sqrt{v^{2}-64h$ . What velocity must a coaster have at the top of a 50-foot hill to achieve a velocity of 57 feet per second.

Answer 1

The velocity that the coaster must have at the top of a 50-foot hill to achieve a velocity of 57 feet per second is 7 feet/second.

What is Velocity?

Velocity is the rate of change of its position with respect to time.

$V = \dfrac{dy}{dt}$

Given the velocity(v) in feet per second of a roller coaster at the bottom of a hill is related to the vertical drop(h) in feet and the velocity(v°) in feet per second of the coaster at the top of the hill by the formula v°=√(v²-64h).

Therefore, the velocity of the coaster at the top should be,

$v^o=\sqrt{(v^2-64h)}\\\\v^o=\sqrt{[57^2-(64\times 50)]}\\\\v^o=\sqrt{49}\\\\v^o = 7\rm\ feet/second$

Hence, the velocity that the coaster must have at the top of a 50-foot hill to achieve a velocity of 57 feet per second is 7 feet/second.

Learn more about Velocity:

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