The velocity, v, of a roller coaster as it moves down a hill is given by the formula
v2 = 64h + vo2 ,
where vo is the initial velocity and h is the vertical drop in feet. The designer of a coaster wants the coaster to have a velocity of 90 feet per second when it reaches the bottom of the hill. The initial velocity of the coaster at the top of the hill is 10 feet per second. Write an equation that models the situation. How high should the designer make the hill?

Question

The velocity, v, of a roller coaster as it moves down a hill is given by the formula
v2 = 64h + vo2 ,
where vo is the initial velocity and h is the vertical drop in feet. The designer of a coaster wants the coaster to have a velocity of 90 feet per second when it reaches the bottom of the hill. The initial velocity of the coaster at the top of the hill is 10 feet per second. Write an equation that models the situation. How high should the designer make the hill?

anonymous · Answer

V^2 = 64*h + Vo^2 --> V^2 - (Vo)^2 = 64*h
At the bottom, the velocity is : V^2 = (90)^2 = 8,100
At the top of the hill, the velocity is : (Vo)^2 = (10)^2 = 100
64*h = 8,100 - 100 = 8.000
The hill should be designed h = 8,000/64 = 125 ft tall.