Wild Roger Rollercoaster (mass of 75 kg) is travelling on a new ride called the Riddler's Revenge. On a 5.1 m hill he is moving along at 32.6 m/s, then slows down to 24.6 m/s on the second hill. How high is the second hill?
+6251 Wild Roger Rollercoaster (mass of 75 kg) is travelling on a new ride called the Riddler's Revenge. On a 5.1 m hill he is moving along at 32.6 m/s, then slows down to 24.6 m/s on the second hill. How high is the second hill?
The way to solve this is by noting that energy on this ideal roller coaster is conserved.
The total energy of the car is the sum of its potential and kinetic energies.
The potential energy at a point at heigh h is given by $$m g h$$
m - mass of the car
g - the gravitational accleration $$9.8 m/s^2$$
h - the height
The kinetic energy at a given speed is given by $$\frac 1 2 m v^2$$
m - the mass
v - the speed
At the first point the total energy is
$$(75)(9.8)(5.1)+\frac 1 2 (75)(32.6)^2=43602 Joules$$
At the second point the car has this same total energy but less of it is kinetic and more of it is potential.
$$43602=(75)(9.8)h_2+\frac 1 2 (75)(24.6)^2\\
43602-22693.5=735 h_2\\
h_2=28.45m$$
