A 250.0 kg roller coaster car has 20,000 J of potential energy at the top of the hill. Neglecting frictional losses, what is the velocity of the car at the bottom of thee hill?

A.) 9.8 m/s
B). 12.6 m/s
C). 14.1 m/s
D). 8.9 m/s

Assuming the car has no kinetic energy at the top...

energy at the bottom = energy at the top
energy at the bottom = kinetic energy
kinetic energy = (1/2) * m * (v^2)
So,
(1/2)*m*(v^2)=20,000J
Solve for v

To find the velocity of the roller coaster car at the bottom of the hill, we can use the principle of conservation of energy. According to this principle, the total energy of a system remains constant as long as there are no external forces doing work on the system.

In this case, the roller coaster car has potential energy at the top of the hill, which gets converted into kinetic energy at the bottom. So we can equate the potential energy at the top with the kinetic energy at the bottom.

The potential energy (PE) of an object can be calculated using the formula:

PE = m * g * h

where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2) and h is the height of the object.

According to the question, the potential energy at the top of the hill is 20,000 J.

PE = 20,000 J
m = 250.0 kg
g = 9.8 m/s^2

Now, we can calculate the height (h) of the hill.

PE = m * g * h
20,000 J = 250.0 kg * 9.8 m/s^2 * h

Solving for h:

h = 20,000 J / (250.0 kg * 9.8 m/s^2)
h = 8.16 m

So, the height of the hill is approximately 8.16 meters.

Now, we can calculate the velocity of the roller coaster car at the bottom of the hill using the following equation:

KE = (1/2) * m * v^2

where KE is the kinetic energy and v is the velocity of the car.

Since the potential energy is converted into kinetic energy at the bottom, we can equate the two:

PE = KE
m * g * h = (1/2) * m * v^2

Canceling out the mass:

g * h = (1/2) * v^2

Solving for v:

v^2 = 2 * g * h
v = √(2 * g * h)

Plugging in the values:

v = √(2 * 9.8 m/s^2 * 8.16 m)
v ≈ 12.6 m/s

Therefore, the velocity of the car at the bottom of the hill is approximately 12.6 m/s.

Hence, the correct answer is B) 12.6 m/s.