Chapter 6, Problem 6RAT

A shiny sports car at the top of a vertical cliff has potential energy of $100\text{MJ}$ relative to the ground below. Unfortunately, a mishap occurs and it falls over the edge. When it is halfway to the ground, its kinetic energy is

(a) The same as its potential energy at that point.

(b) negligible.

(c) about $60\text{MJ}$.

(d) more than $60\text{MJ}$.

To determine

The correct option for the statement “A shiny sports car at the top of a vertical cliff has potential energy of $100\text{MJ}$ relative to the ground below. Unfortunately, a mishap occurs and it falls over the edge. When it is halfway to the ground, its kinetic energy is”.

Answer to Problem 6RAT

The correct option for the statement “A shiny sports car at the top of a vertical cliff has potential energy of $100\text{MJ}$ relative to the ground below. Unfortunately, a mishap occurs and it falls over the edge. When it is halfway to the ground, its kinetic energy is” is option (a).

Explanation of Solution

According to the law of conservation of energy, whenever there is decrease in one form of energy in an isolated system, there would be identical increase in another form of energy

As a shiny sport car at the top of a vertical Cliff at a height $h$, has energy $100\text{ MJ}$, then at half of the distance the energy is half of its value at $h$, so the potential energy at height half is $50\text{ MJ}$.

According to the law of conservation of energy, the sum of kinetic energy at halfway and potential energy at halfway should be equal to potential energy at the top of the cliff.

Conclusion:

Therefore, the correct option for the statement “A shiny sports car at the top of a vertical cliff has potential energy of $100\text{MJ}$ relative to the ground below. Unfortunately, a mishap occurs and it falls over the edge. When it is halfway to the ground, its kinetic energy is” is option (a).