Question

A $90kg$ firefighter needs to climb the stairs of a $20m$-tall building while carrying a $40kg$ backpack filled with gear. How much power does he need to reach the top in $55s$?

Short answer

The power need to reach the top in$55s$is$460W$

Step-by-step solution

Content Introduction

Power is the rate of doing work. It is calculated as

$P=\frac{W}{t}$

Work done is the dot product of force and displacement.

$$\begin{gathered} W_{\left(\overrightarrow{F}\right)}=\overrightarrow{F}.\overrightarrow{d} \\ {W}_{\left(\overrightarrow{F}\right)}=Fd\cos \left(\theta \right) \end{gathered}$$

Substitute $mgfor{F}_g$and $180°$for $\theta$.

$$\begin{gathered} W_{\left(\overrightarrow{F}\right)}=mgd\left(\cos \left(180°\right)\right) \\ {W}_{\left(\overrightarrow{F}\right)}=-mgd \end{gathered}$$

Hence, work done by firefighter is equal to negative of potential energy.

Content Explanation

The power need to reach the top in $55s$is

$$\begin{gathered} P=\frac{mgd}{t} \\ P=\frac{(130kg)(9.8m/s)(20m)}{55s} \\ P=460W \end{gathered}$$