6. Steel Phantom is a roller coaster in Pennsylvania that, like the Desperado in

Question

6. Steel Phantom is a roller coaster in Pennsylvania that, like the Desperado in Nevada, has a vertical drop of 68.6 m. Suppose a roller-coaster car with a mass of 1.00 x 10^3 kg travels from the top of that drop without friction. The car then decelerates along a horizontal stretch of track until it comes to a stop. How long does it take the car to decelerate if the constant force acting on it is -2.24 x 10^4 N? How far does the car travel along the horizontal track before stopping? Assume the car's speed at the peak of the drop is zero.

Explanation / Answer

speed at the bottom = v

conservation of energy

0.5*mv^2 = m*g*h

v = sqrt(2*g*h)

v = sqrt(2*9.8*68.6) = 36.668 m/s

K = F*d

0.5*mv^2 = F*d

0.5*1x10^38*36.668^2 = 2.24x10^4*d

d = 30.0125 m

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