What is the speed at the exit (height of zero)?

Question

A roller coaster is built with four "humps." The humpr from which the coaster is launced is 40 m tall, the second is 30 m, the third is 20 m and the fourth is 10 m. Assuming the coaster is launced with negligible initial speed, what is the speed at the top of each hump? What is the speed at the exit at a height of zero?

Answer 1

Start by setting up a conservation of energy equation:

.5*m*v^2=m*g*d
where d is the difference in height

simplify to solve for v:
v=Sqrt(2*g*d)

Since we are ignoring friction, the speeds will progressively increase:

30
v=sqrt(2*g*(40-30))
14.0 m/s

20
v=sqrt(2*g*(40-20))
19.8 m/s

10
v=sqrt(2*g*(40-10))
24.3 m/s

0
v=sqrt(2*g*40)
28.0 m/s


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