Students design a model roller-coaster track. they place a rubber ball at the highest point on the track and let it go. the ball rolls along the track pulled only by the force of gravity. eventually, it comes to a stop. which change to the design will result in the ball moving the greatest distance?

Raising the highest point of the track to a higher point

Explanation:

When the rubber ball starts its motion, from the highest point of the track, it has only gravitational potential energy, given by:

where m is the mass of the ball, g is the gravitational acceleration and h is the height above the ground.

As the ball descends the track, this potential energy is partially converted into kinetic energy, given by:

(where m is the mass and v is the speed)

and partially lost as heat, due to the friction between the surface of the track.

As a consequence, the higher the initial height of the track (h in the formula), the greater will be the kinetic energy gained by the ball. A greater kinetic energy means a larger velocity, which also means that the ball will cover a longer distance before stopping.

the total distance traveled by the car is

30km + 49km = 79 km .