Sure! Let's use the provided data to complete the given paragraph:
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.
First, we determine Susan's kinetic energy. The formula for kinetic energy (KE) is given by:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
For Susan:
[tex]\[ KE_{\text{Susan}} = \frac{1}{2} \times 25 \times (10)^2 \][/tex]
[tex]\[ KE_{\text{Susan}} = \frac{1}{2} \times 25 \times 100 \][/tex]
[tex]\[ KE_{\text{Susan}} = \frac{1}{2} \times 2500 \][/tex]
[tex]\[ KE_{\text{Susan}} = 1250 \, \text{joules} \][/tex]
Next, we determine Hannah's kinetic energy using the same formula:
For Hannah:
[tex]\[ KE_{\text{Hannah}} = \frac{1}{2} \times 30 \times (8.5)^2 \][/tex]
[tex]\[ KE_{\text{Hannah}} = \frac{1}{2} \times 30 \times 72.25 \][/tex]
[tex]\[ KE_{\text{Hannah}} = \frac{1}{2} \times 2167.5 \][/tex]
[tex]\[ KE_{\text{Hannah}} = 1083.75 \, \text{joules} \][/tex]
From these calculations:
- Susan's kinetic energy is 1250 joules.
- Hannah's kinetic energy is 1083.75 joules.
Finally, we compare the kinetic energies:
- Since 1250 joules (Susan's kinetic energy) is greater than 1083.75 joules (Hannah's kinetic energy), we can conclude:
Susan's Kinetic energy is greater than Hannah's because Susan's kinetic energy (1250 joules) is greater than Hannah's kinetic energy (1083.75 joules).
Therefore, the paragraphs should be correctly filled in the following way:
- Susan's kinetic energy is 1250 joules.
- Susan's kinetic energy is greater than Hannah's because Susan's kinetic energy (1250 joules) is greater than Hannah's kinetic energy (1083.75 joules).
