Let's solve the problem step-by-step:
1. Understanding the given information:
- The kinetic energy (KE) of the ball after 6.00 seconds is [tex]\(23.8 \, \text{J}\)[/tex].
- The total mechanical energy (E) of the ball during the drop is [tex]\(256 \, \text{J}\)[/tex].
2. Applying the principle of conservation of mechanical energy:
- According to the principle of conservation of mechanical energy, the total mechanical energy of a system is the sum of its potential energy (PE) and kinetic energy (KE).
[tex]\[
E = PE + KE
\][/tex]
3. Rearranging the formula to solve for potential energy (PE):
- We can find the potential energy by rearranging the formula:
[tex]\[
PE = E - KE
\][/tex]
4. Substituting the given values:
- Substitute [tex]\( E = 256 \, \text{J} \)[/tex] and [tex]\( KE = 23.8 \, \text{J} \)[/tex] into the equation:
[tex]\[
PE = 256 \, \text{J} - 23.8 \, \text{J}
\][/tex]
5. Performing the subtraction:
- Compute the difference:
[tex]\[
PE = 256 \, \text{J} - 23.8 \, \text{J} = 232.2 \, \text{J}
\][/tex]
6. Final result:
- The potential energy (PE) of the ball at this point is:
[tex]\[
PE = 232.2 \, \text{J}
\][/tex]
In conclusion, the potential energy of the ball after 6.00 seconds is [tex]\( 232.2 \, \text{J} \)[/tex].
