The speed of the roller-coaster car at the bottom of the track is determined by the conversion of potential energy at the top of the track to kinetic energy at the bottom. The potential energy at the top is given by m*g*h, 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 1/2*m*v^2, where v is the speed of the car.

Setting these two equal to each other (since energy is conserved), we get:

m*g*h = 1/2*m*v^2

Solving for v, we get:

v = sqrt(2*g*h)

If the height h is increased by a factor of 5, the new speed v' is given by:

v' = sqrt(2*g*5h) = sqrt(5)*sqrt(2*g*h) = sqrt(5)*v

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

Question

The speed of the roller-coaster car at the bottom of the track is determined by the conversion of potential energy at the top of the track to kinetic energy at the bottom. The potential energy at the top is given by m*g*h, 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 1/2*m*v^2, where v is the speed of the car.

Setting these two equal to each other (since energy is conserved), we get:

m*g*h = 1/2*m*v^2

Solving for v, we get:

v = sqrt(2*g*h)

If the height h is increased by a factor of 5, the new speed v' is given by:

v' = sqrt(2*g*5h) = sqrt(5)*sqrt(2*g*h) = sqrt(5)*v

So the speed at the bottom increases by a factor of sqrt(5), which is approximately 2.24. So 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 conversion of potential energy at the top of the track to kinetic energy at the bottom. The potential energy at the top is given by m*g*h, 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 1/2*m*v^2, where v is the speed of the car.

Setting these two equal to each other (since energy is conserved), we get:

m*g*h = 1/2*m*v^2

Solving for v, we get:

v = sqrt(2*g*h)

If the height h is increased by a factor of 5, the new speed v' is given by:

v' = sqrt(2*g*5h) = sqrt(5)*sqrt(2*g*h) = sqrt(5)*v

So the speed at the bottom increases by a factor of sqrt(5), which is approximately 2.24. So 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? 5.00 7.50 25.0 2.24

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