Question

A rollercoaster applies 36000N of force to a 2600kg train of coaster cars for 2 seconds to launch the coaster up the first hill. The launch platform is 3 meters above the ground. How much work did the launcher do and what is the maximum height of the first hill on the rollercoaster if the coaster still has a velocity of 0.25 m/s at the top of the first hill?

Answer 1

$$Ft=mv\to 36000(2)=2600v\\v=27.69\frac{m}{s}$$

$$W=0.5mv^2=0.5(2600)(27.69)^2=996757\ J$$

$$v^2-u^2=2gh\\27.69^2-0.25^2=2(9.8)h\\h=39\ m$$

$$H=39+3=42\ m$$