Determine the required height h of the roller coaster so that when it is essentially at rest at the crest of the hill A it will reach a speed of 100km/h when it comes to the bottom B. Also, what should be the minimum radius of curvature p for the track at B so that the passengers do not experience a normal force greater than 4mg

a) 39.37 m

b) 26.25 m

Explanation:

Given

speed of the roller coaster, v = 100 km/h = 100 * (1000/3600) m/s = 27.78 m/s

Using the law of conservation of energy.

Potential Energy = Kinetic Energy

mgh = 1/2mv²

gh = 1/2v²

h = v²/2g

h = 27.78² / 2 * 9.8

h = 771.7284 / 19.6

h = 39.37 m

Also,

kmg - mg = mv²/p

kg - g = v²/p

p = v²/g (k - 1)

p = 27.78² / 9.8 (4 - 1)

p = 771.7284 / 29.4

p = 26.25 m

Therefore, the height of the roller coaster is 39.37 m and the radius of curvature required is 26.25 m