Sure, let's solve this step-by-step.
1. Identify the Given Data:
- Vertical drop of the water slide (height, [tex]\( h \)[/tex]): 49 meters
- Mass of George ([tex]\( m \)[/tex]): 90 kg
- Kinetic energy at ground level ([tex]\( KE \)[/tex]): 21,000 Joules
- Gravitational constant ([tex]\( g \)[/tex]): 9.8 m/s[tex]\(^2\)[/tex]
2. Calculate the Potential Energy at the Top of the Slide:
Potential energy ([tex]\( PE \)[/tex]) at the top of the slide is given by the formula:
[tex]\[
PE = m \cdot g \cdot h
\][/tex]
Substituting the given values:
[tex]\[
PE = 90 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 49 \, \text{m}
\][/tex]
[tex]\[
PE = 90 \times 9.8 \times 49
\][/tex]
[tex]\[
PE = 43218 \, \text{Joules}
\][/tex]
3. Calculate the Energy Converted into Heat:
The energy converted into heat is the difference between the potential energy at the top and the kinetic energy at the bottom:
[tex]\[
\text{Energy converted to heat} = PE - KE
\][/tex]
Substituting the known values:
[tex]\[
\text{Energy converted to heat} = 43218 \, \text{Joules} - 21000 \, \text{Joules}
\][/tex]
[tex]\[
\text{Energy converted to heat} = 22218 \, \text{Joules}
\][/tex]
Therefore, the energy converted into heat when George reaches ground level is [tex]\( 22,218 \)[/tex] joules.
