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A ball is dropped from the roof of a building. After 4 seconds, the ball has 192 J of potential energy. The total mechanical energy of the drop is 321 J.

What is the kinetic energy of the ball at this point?

[tex]\( KE = [?] \, J \)[/tex]

[tex]\( E = PE + KE \)[/tex]



Answer :

GinnyAnswer
To determine the kinetic energy of the ball at this point, we start by understanding the given information and the relevant formulas.

We know the following:
1. The potential energy ([tex]\(PE\)[/tex]) of the ball is [tex]\(192\)[/tex] Joules.
2. The total mechanical energy ([tex]\(E\)[/tex]) of the system is [tex]\(321\)[/tex] Joules.
3. The relationship between mechanical energy, potential energy, and kinetic energy ([tex]\(KE\)[/tex]) is described by the equation:
[tex]\[ E = PE + KE \][/tex]
4. We aim to find the kinetic energy ([tex]\(KE\)[/tex]) of the ball.

Here are the steps to find the kinetic energy:

1. Write down the mechanical energy equation:
[tex]\[ E = PE + KE \][/tex]

2. Rearrange this equation to solve for the kinetic energy ([tex]\(KE\)[/tex]):
[tex]\[ KE = E - PE \][/tex]

3. Substitute the given values into the equation:
[tex]\[ KE = 321 \, J - 192 \, J \][/tex]

4. Perform the subtraction:
[tex]\[ KE = 129 \, J \][/tex]

Therefore, the kinetic energy of the ball at this point is [tex]\(129\)[/tex] Joules.

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