Question

A man of mass 60 kg runs up a flight of 30 steps in 40 sec. if each step is 20 cm high, calculate the power of the man? ​

Answer 1

$Mass \: of \: man \: = \: 60 kg$

$total \: steps \: covered \: = 30$

$height \: of \: each \: step \: = 20 \: cm$

$height \: of \: all \: steps \: = 30 \times 20$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: :⟹ \: 600 \: cm = 6m$

$\: \: \: \: \: \: \boxed{ \bold \red{power = \frac{workdone}{time} } }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : ⟹ \: \: \: \: \frac{mgh}{t} \\ \:\:\:\:\:\:\: \: \: \: \: \: \: \: \: \: \: \: \green{using\: g=10m/s}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : ⟹ \: \frac{60 \times 10 \times 6}{40}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : ⟹ \: \: \: \: \: \: \frac{3600}{40}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : ⟹ \: \: \: \: \: \: \: 90 \: watt$

$\orange{please \: mark \: as \: brainliest............}$

Answer 2

$\bigstar$ Given

A man of mass 60 kg runs up a flight of 30 steps in 40 seconds

Each step is 20 cm high

$\bigstar$ To Find

Power of the man

$\bigstar$ Solution

We know that

$\red{\sf \longrightarrow P=\dfrac{W}{t}}$

$\green{\sf \longrightarrow W=mgh}$

Hence

Equating the values of 'W'

We get

$\pink{\sf \longrightarrow P=\dfrac{W}{t}=\dfrac{mgh}{t}}$

Here

• P  = Power
• W = Work done
• m = Mass
• g  = Acceleration of gravity
• h  = Height
• t   = Time

Units

• P  = Watt (W)
• W = Joule (J)
• m = kilogram (kg)
• g  = m/s²
• h  = metre (m)
• t   = seconds (s)

According to the question

We are asked to find the power of the man

Hence

We must find "P"

Therefore

$\purple{\sf \longrightarrow P=\dfrac{mgh}{t}}$

Given that

A man of mass 60 kg runs up a flight of 30 steps in 40 seconds

Each step is 20 cm high

Hence

• m = 60 kg
• h = 30 × 20 cm = 600 cm = 6 m
• t = 40 s

We know that

• g = 10 m/s²

Substituting the values

We get

$\blue{\sf \longrightarrow P=\dfrac{60 \times 10 \times 6}{40} \ W}$

$\orange{\sf \longrightarrow P=\dfrac{60 \times 60}{40} \ W}$

$\red{\sf \longrightarrow P=\dfrac{3600}{40} \ W}$

$\pink{\sf \longrightarrow P=\dfrac{360}{4} \ W}$

Therefore

$\purple{\sf \longrightarrow P= 90 \ W}$

Hence

$\checkmark$ Power of the man = 90 W