mrs rossow ran the Yakima river cayons marathon the course is 27.2 miles long and it took her 2 hours and 15 minutes to finish if she weighs 135pounds calculate the work and power she used.
A.work
B.power
To calculate the work done by Mrs. Rossow during the marathon, we need to know her weight and the distance she covered.
Work (W) is defined as the force applied over a distance. In this case, the force is her weight (mass multiplied by gravity) and the distance is the length of the marathon course.
The formula for calculating work is:
W = Force x Distance
First, let's calculate her weight in Newtons. Assuming she weighs 135 pounds, we need to convert it to kilograms since the standard unit of mass in the metric system is kilograms.
1 pound = 0.453592 kilograms
So, Mrs. Rossow's weight in kilograms is:
135 pounds * 0.453592 kilograms/pound = 61.23508 kilograms
To find the force, we multiply her weight by the acceleration due to gravity (9.8 m/s^2):
Force = 61.23508 kg * 9.8 m/s^2 = 600.550984 N (rounded to three decimal places)
Now that we have the force and distance, we can calculate the work:
Work = Force x Distance = 600.550984 N * 27.2 miles
However, we need to convert the distance from miles to meters since the unit of distance used in the formula for work is meters:
1 mile = 1609.34 meters
So, the distance in meters is:
27.2 miles * 1609.34 meters/mile = 43796.7488 meters (rounded to four decimal places)
Finally, we can calculate the work:
Work = 600.550984 N * 43796.7488 meters = 26295235.98 joules (rounded to two decimal places)
Therefore, Mrs. Rossow used approximately 26,295,235.98 joules of work to complete the marathon.
Now let's calculate the power:
Power (P) is defined as the rate at which work is done. It can be calculated by dividing the work done by the time taken.
The formula for calculating power is:
P = Work / Time
We know the work (26,295,235.98 joules) and the time taken (2 hours and 15 minutes).
First, we need to convert the time to seconds:
2 hours = 2 * 60 minutes = 120 minutes
15 minutes = 15 minutes
Total time in seconds = 120 minutes * 60 seconds/minute + 15 seconds = 7200 seconds + 15 seconds = 7215 seconds
Now we can calculate the power:
Power = Work / Time = 26,295,235.98 joules / 7215 seconds
Power = 3641.963573 watts (rounded to three decimal places)
Therefore, Mrs. Rossow used approximately 3641.963573 watts of power to complete the marathon.