Answer :
To find out how many calories a 205 lb person uses to climb 3 flights of stairs to a height of 50 meters, we can follow these steps:
1. Convert Weight to Kilograms:
- First, we need to convert the person's weight from pounds to kilograms.
- We use the conversion factor: 1 pound = 0.453592 kilograms.
- So, the weight in kilograms is: `205 lbs × 0.453592 kg/lb = 93.0 kg`.
2. Calculate the Work Done:
- Work done can be computed using the formula: [tex]\( W = m \times g \times h \)[/tex].
- Where:
- [tex]\( m \)[/tex] is the mass in kilograms (which we found to be 93.0 kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity (9.8 m/s²),
- [tex]\( h \)[/tex] is the height climbed (50 meters).
- Substituting the values, we get:
[tex]\( W = 93.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 50 \, \text{m} = 45570 \, \text{joules}\)[/tex].
3. Convert Joules to Calories:
- To convert energy from joules to calories, we use the conversion: 1 calorie = 4.184 joules.
- So, the energy in calories is:
[tex]\( \frac{45570 \, \text{joules}}{4.184 \, \text{joules/cal}} = 10889.9 \, \text{calories}\)[/tex].
Therefore, the 205 lb person uses approximately 10890 calories to climb to a height of 50 meters. Among the given options, the choice closest to this calculated value is 10913 cal.
1. Convert Weight to Kilograms:
- First, we need to convert the person's weight from pounds to kilograms.
- We use the conversion factor: 1 pound = 0.453592 kilograms.
- So, the weight in kilograms is: `205 lbs × 0.453592 kg/lb = 93.0 kg`.
2. Calculate the Work Done:
- Work done can be computed using the formula: [tex]\( W = m \times g \times h \)[/tex].
- Where:
- [tex]\( m \)[/tex] is the mass in kilograms (which we found to be 93.0 kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity (9.8 m/s²),
- [tex]\( h \)[/tex] is the height climbed (50 meters).
- Substituting the values, we get:
[tex]\( W = 93.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 50 \, \text{m} = 45570 \, \text{joules}\)[/tex].
3. Convert Joules to Calories:
- To convert energy from joules to calories, we use the conversion: 1 calorie = 4.184 joules.
- So, the energy in calories is:
[tex]\( \frac{45570 \, \text{joules}}{4.184 \, \text{joules/cal}} = 10889.9 \, \text{calories}\)[/tex].
Therefore, the 205 lb person uses approximately 10890 calories to climb to a height of 50 meters. Among the given options, the choice closest to this calculated value is 10913 cal.
