a girl of mass 60kg runs up a flight of 50 stairs, each measuring 20cm, in 60 seconds. Calculate the power of the girl
Answers
Given :
Mass of the girl = 60 kg
Total Number of stairs = 50
Height of each one = 20 cm
Time taken = 60 sec
To Find :
Power of the girl
Solution :
Height of each stair = 20 cm = 0.2 m
Total height of the staircase = Number of stairs × height of each stair = 50 × 0.2 = 10 m
Expression for Power is given by ,
\begin{gathered} \\ : \implies \sf \: P = \frac{mgh}{t} \end{gathered}
:⟹P=
t
mgh
We have ,
m = 60 kg
g = 9.8 m/s²
t = 60 sec
h = 10 m
Now by substituting the values we get ;
\begin{gathered} \\ : \implies \sf \: P = \frac{(60 \: kg)(9.8 \: ms {}^{ - 2} )(10 \: m)}{(60 \: s)} \\ \end{gathered}
:⟹P=
(60s)
(60kg)(9.8ms
−2
)(10m)
\begin{gathered} \\ : \implies \sf \: P = \frac{600 \: kgm {}^{2} (9.8)}{60 \: s {}^{ - 3} } \\ \end{gathered}
:⟹P=
60s
−3
600kgm
2
(9.8)
\begin{gathered} \\ : \implies \sf \: P = \frac{5800}{60} \: kgm {}^{2} {s}^{ - 3} \\ \end{gathered}
:⟹P=
60
5800
kgm
2
s
−3
\begin{gathered} \\ : \implies{\underline{\boxed{\sf { \: P = \:98 \: W }}}}\end{gathered}
:⟹
P=98W
Hence , The Power of the girl is 98 W.
Answer: