3. A roller-coaster car is moving over the top of a hill. At the instant it is on the hill top, it has a kinetic energy of E and a gravitational potential energy of 3E. When it coasts down to ground level, if total mechanical energy is conserved, what is the kinetic energy of the car on the ground?
(A) 4E (B) 3E (C) 2E (D) E

The correct option is (b).

Explanation:

Given that,

At the top of the hill, the kinetic energy is E and the gravitational potential energy is 3E.

We need to find the kinetic energy of the car on the ground.

We know that,

Mechanical energy = kinetic energy + potential energy

According to the law of conservation of energy, the total mechanical energy is conserved.

It means, when it coasts down to ground level, the kinetic energy is same as that on the top of the hill. Hence, the required kinetic energy on the ground is equal to 3E.

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