The distance the springs need to bring the car to a stop can be calculated using the equation for the potential energy of an object at a height, which is:
PE = mgh
where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
In this case, the car has a mass of 1,836 kg and is at a height of 88.6 meters. So the potential energy of the car at the top of the roller coaster is:
PE = 1,836 kg * 9.8 m/s^2 * 88.6 m = 1.5*10^5 J
Next, we need to find the work done by the spring. Work can be calculated using the equation
W = 1/2 * kx^2
where k is the spring constant (100,000 N/m) and x is the compression distance of the spring.
Since the work done by the spring is equal to the potential energy of the car, we can set the two equations equal to each other and solve for x (the compression distance of the spring):
1/2 * kx^2 = 1.510^5 J
x = sqrt(2 * 1.510^5 J / 100,000 N/m)
x = sqrt(30000/100000)
x = 0.173 m
Therefore, the spring needs a distance of 0.173 m to bring the car to a stop.