Performance 66404

A person weighing 50 kg can climb 15 stairs. One step is 18 cm high. Determine a person's performance when:
a) slowly climbing the stairs if it took him 13 seconds
b) going down the stairs slowly if it took him 10 seconds
c) quickly climbing the stairs if it took him 7 seconds

Correct answer:

P₁ =  101.8731 W
P₂ =  132.435 W
P₃ =  189.1929 W

Step-by-step explanation:

$$\begin{gathered} m=50\text{kg} \\ s=18\text{cm}\to \text{m}=18:100\text{m}=0.18\text{m} \\ n=15 \\ h=n\cdot s=15\cdot 0.18=\frac{27}{10}=2.7\text{m} \\ g=9.81{\text{m/s}}^2 \\ E=m\cdot g\cdot h=50\cdot 9.81\cdot 2.7=\frac{26487}{20}=1324.35\text{J} \\ {t}_1=13\text{s} \\ {P}_1=E/t_1=1324.35/13=101.8731\text{W} \end{gathered}$$

$$\begin{gathered} t_2=10\text{s} \\ {P}_2=E/t_2=1324.35/10=132.435\text{W} \end{gathered}$$

$$\begin{gathered} t_3=7\text{s} \\ {P}_3=E/t_3=1324.35/7=189.1929\text{W} \end{gathered}$$

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