Question

Given a ball moving in free fall between two heights. The ball moves from an initial height to some final height while still moving. If the initial gravitational potential energy of the ball is 5.00 J and the initial kinetic energy of the ball is 5.00 J then if the final gravitational potential energy of the ball is 2.00 J then what is the final kinetic energy of the ball? A) 2.00 JB) 5.00 JC) 8.00 JD) 106 JE) 10.0 j

Answer 1

C) 8.00 J

Step-by-step explanation

Given:

• The initial gravitational potential energy, 5.00 J

,

• The initial kinetic energy, 5.00 J

,

• The final gravitational potential energy, 2.00 J

Unknown:

• The final kinetic energy

By the law of conservation of energy, we know that the total mechanical energy must be conserved.

A ball moving in free fall only has gravitational potential energy and kinetic energy. The sum of the two must be constant for all heights,

`PE_i+KE_i=PE_f+KE_f`

Replace with the known values,

`\begin{gathered} 5.00J+5.00J=2.00J+KE_f \\ 10.00J=2.00J+KE_f \end{gathered}`

Solving for the final kinetic energy,

`KE_f=10.00J-2.00J=8.00J`

Hence, the final kinetic energy of the ball is 8.00 J