Question

A computational model predicts the maximum speed that a roller coaster car can experience, given its mass and initial height and speed. What is the maximum speed when the conditions are mass = 450 kg, initial height = 30 m, and the roller coaster car is initially at rest?
a) 24.2 m/s

b) 93.9 m/s

c) 132,300 m/s

d) 30 m/s

Answer 1

Assuming no friction between the roller coaster car and the hill, and neglecting air resistance, the kinetic energy the roller coaster car would have at the bottom of the hill would be equal to its gravitational potential energy at the top of the hill, by conservation of energy.

At the top of the hill, the roller coaster car only contains potential energy as it is perfectly still, so its total mechanical energy at the top of the hill would be in the form of only potential energy.

At the bottom of the hill, this potential energy would have converted all into kinetic energy, because there are, in this highly ideal situation, no energy losses due to friction.

The law of conservation of mechanical energy states that the total mechanical energy in a system is always conserved.

Let KE denote Kinetic Energy

As an equation, the relationship would be:

mgh=1/2mv^2

OR

KE=mgh

Assuming the acceleration due to gravity near the earth's surface is 9.81ms, our equation becomes:

Now, mgh = 1/2 mv^2

gh=1/2v^2

or;

v= √2gh

Now, v =√2 . 9.81 . 30

Therefore, v=24.2m/s

Hence option A is correct