The speed of the roller-coaster car at the bottom of the track is determined by the potential energy it has at the top of the track, which is converted into kinetic energy as it falls. The potential energy is given by mgh, where m is the mass of the car, g is the acceleration due to gravity, and h is the height of the track. The kinetic energy at the bottom is given by 1/2mv^2, where v is the speed of the car.

If the height of the track is increased by a factor of 5, the potential energy at the top is increased by the same factor. Since all this energy is converted into kinetic energy at the bottom, the kinetic energy at the bottom also increases by a factor of 5.

However, the speed of the car is the square root of the kinetic energy (since v = sqrt(2KE/m)). Therefore, if the kinetic energy increases by a factor of 5, the speed increases by a factor of sqrt(5).

So, the speed at the bottom will increase by a factor of sqrt(5), which is approximately 2.24. Therefore, the correct answer is 2.24.

Question

The speed of the roller-coaster car at the bottom of the track is determined by the potential energy it has at the top of the track, which is converted into kinetic energy as it falls. The potential energy is given by mgh, where m is the mass of the car, g is the acceleration due to gravity, and h is the height of the track. The kinetic energy at the bottom is given by 1/2mv^2, where v is the speed of the car.

If the height of the track is increased by a factor of 5, the potential energy at the top is increased by the same factor. Since all this energy is converted into kinetic energy at the bottom, the kinetic energy at the bottom also increases by a factor of 5.

However, the speed of the car is the square root of the kinetic energy (since v = sqrt(2KE/m)). Therefore, if the kinetic energy increases by a factor of 5, the speed increases by a factor of sqrt(5).

So, the speed at the bottom will increase by a factor of sqrt(5), which is approximately 2.24. Therefore, the correct answer is 2.24.

Knowee AI · Accepted Answer

The speed of the roller-coaster car at the bottom of the track is determined by the potential energy it has at the top of the track, which is converted into kinetic energy as it falls. The potential energy is given by mgh, where m is the mass of the car, g is the acceleration due to gravity, and h is the height of the track. The kinetic energy at the bottom is given by 1/2mv^2, where v is the speed of the car.

If the height of the track is increased by a factor of 5, the potential energy at the top is increased by the same factor. Since all this energy is converted into kinetic energy at the bottom, the kinetic energy at the bottom also increases by a factor of 5.

However, the speed of the car is the square root of the kinetic energy (since v = sqrt(2KE/m)). Therefore, if the kinetic energy increases by a factor of 5, the speed increases by a factor of sqrt(5).

So, the speed at the bottom will increase by a factor of sqrt(5), which is approximately 2.24. Therefore, the correct answer is 2.24.

A roller-coaster car rolls down a track, reaching a speed of v0 at the bottom. If the height of the track is increased by a factor of 5.00, assuming the track is frictionless, by what factor will the speed at the bottom increase? 7.50 25.0 5.00 2.24

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