Question

A boy leaving weight of 55kg goes upstairs of heigth 4.5m in 3.5sec.How much average power is required to the boy?​

Answer 1

$\large \underline \bold{Given}$:-

ㅤㅤㅤ weight = 55 kg

ㅤㅤㅤ height = 4.5 m

ㅤㅤㅤㅤ time = 3.5 sec.

$\large \underline \bold{To \: Find}$:-

ㅤhow much average power is

ㅤㅤ required to the boy ?

$\large \underline \bold{Usable \: Formula}$:-

ㅤㅤㅤㅤㅤ$\large\boxed{\sf\red{U = mgh}}$

ㅤㅤㅤㅤㅤ$\large\boxed{\sf\red{P = \dfrac{U}{t}}}$

here ,

ㅤㅤㅤㅤU = energy/work (in joule)

ㅤㅤㅤㅤm = weight (in kg)

ㅤㅤㅤㅤh = height (in metre)

ㅤㅤㅤㅤP = power (in Watt)

ㅤㅤㅤㅤt = time (in second)

$\large \underline \bold{Solution}$:-

Firstly ,

ㅤㅤㅤU = 55 × 10 × 4.5

ㅤㅤㅤU = 55 × 45

ㅤㅤㅤU = (50 + 5)(50 - 5)

ㅤㅤㅤU = (50)² - (5)²

ㅤㅤㅤU = 2500 - 25

ㅤㅤㅤU = 2475 joule

Now ,

ㅤㅤㅤ$\small \bold{P = \dfrac{2475}{3.5}}$

ㅤㅤㅤ$\sf{P = \dfrac{2475}{(\dfrac{7}{2})}}$

ㅤㅤㅤ$\sf{P = \dfrac{2475\times 2}{7}}$

ㅤㅤㅤ$\sf{P = \dfrac{4950}{7}}$

ㅤㅤㅤ$\small \bold{P = 707.14 \: Watt}$