Discover how IDNLearn.com can help you find the answers you need quickly and easily. Discover trustworthy solutions to your questions quickly and accurately with help from our dedicated community of experts.

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]


Sagot :

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.