Let's break down and calculate the kinetic energy for both Susan and Hannah using the formula [tex]\( KE = \frac{1}{2} m v^2 \)[/tex].
### For Susan:
1. Susan's mass [tex]\( m \)[/tex] is 25 kilograms.
2. Susan's velocity [tex]\( v \)[/tex] is 10 meters/second.
Using the kinetic energy formula:
[tex]\[ KE_{Susan} = \frac{1}{2} \times 25 \times (10)^2 \][/tex]
[tex]\[ KE_{Susan} = \frac{1}{2} \times 25 \times 100 \][/tex]
[tex]\[ KE_{Susan} = 0.5 \times 25 \times 100 \][/tex]
[tex]\[ KE_{Susan} = 1250 \, \text{joules} \][/tex]
### For Hannah:
1. Hannah's mass [tex]\( m \)[/tex] is 30 kilograms.
2. Hannah's velocity [tex]\( v \)[/tex] is 8.5 meters/second.
Using the kinetic energy formula:
[tex]\[ KE_{Hannah} = \frac{1}{2} \times 30 \times (8.5)^2 \][/tex]
[tex]\[ KE_{Hannah} = \frac{1}{2} \times 30 \times 72.25 \][/tex]
[tex]\[ KE_{Hannah} = 0.5 \times 30 \times 72.25 \][/tex]
[tex]\[ KE_{Hannah} = 1083.75 \, \text{joules} \][/tex]
### Comparison:
Susan's kinetic energy is 1250 joules, while Hannah's kinetic energy is 1083.75 joules.
Since [tex]\( 1250 > 1083.75 \)[/tex], Susan's kinetic energy is greater than Hannah's. Therefore, the completed paragraph will be:
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Susan and Hannah are each riding a swing. Susan has a mass of 25 kilograms, and Hannah has a mass of 30 kilograms. Susan's swing moves with a velocity of 10 meters/second, while Hannah's swing moves with a velocity of 8.5 meters/second. Susan's kinetic energy is 1250 joules. Susan's kinetic energy is greater than Hannah's because 1250 joules is greater than 1083.75 joules.
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To summarize:
-Susan's kinetic energy is 1250 joules.
-Susan's kinetic energy is greater than Hannah's because 1250 joules is greater than 1083.75 joules.
