Question

A frictionless roller-coaster is given a maximum possible initial speed v0= 9.1 m/s when it is at height y0 = 6 m above the ground and moves freely afterwards, see figure below. What will be the roller-coaster’s speed when it reaches the lowest point at y1 = 4.4 m?

Answer 1

Step-by-step explanation:

The equation of motion for a frictionless roller coaster is given by: v2 = v02 + 2ay, where v0 is the initial velocity, a is the acceleration due to gravity (9.8 m/s2), and y is the height.

Plugging in the given values of v0, y0 and y1, we get: v2 = 92 + 2(9.8)(-2.6) = 77.88 m/s2.

Therefore, the speed of the roller coaster at the lowest point (y1) will be v = √77.88 m/s = 8.82 m/s.