Question

A boy of mass 50kg can climb a mountain of height 30 m in 5minute.
what will be his power?

Answer 1

${\large{\pmb{\sf{\underline{RequirEd \: solution...}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Provided \: that...}}}}}$

⋆ Mass of a boy = 50 kilograms (Given)

⋆ Height of mountain = 30 metres (Given)

⋆ Time taken = 5 minutes (Given)

⋆ Power = ? (To find)

${\bigstar \:{\pmb{\sf{\underline{Solution...}}}}}$

⋆ A boy of mass 50 kg can climb a mountain of height 30 m in 5 minute. What will be his power?

• His power will be 50 Joules

${\bigstar \:{\pmb{\sf{\underline{Knowledge \: required...}}}}}$

➟ Work - If a body get displaced when a force acts on it, work it said to be done. Work is measured by the product of force and displacement of the body along the direction of force. If a body get displaced by s when a force f act's on it, then the work w be ${\small{\underline{\boxed{\sf{FS \: cos \theta}}}}}$

(Where, Ø denotes angle between force and displacement)

⋆ If both force and displacement are in the same direction, then W = FS.

⋆ Don't forget that work is a scaler quantity and it's SI unit is Joule.

➟ Energy = Capacity of doing work by a body is called it's energy. Energy is a scaler quantity & it's SI unit is ${\sf{joule}}$ Energy developed in a body due to work done on it is called mechanical energy. Mechanical energy is basically of two types -

⑴ Potential energy

⑵ Kinetic energy

➟ Potential energy = The capacity of doing work developed in a body due to it's position or configuration is known as potential energy like, ⑴ energy of stretched or compressed string ⑵ energy of spring in a watch ⑶ energy of water collected at a height.

⋆ PE of a body is the gravitational field of earth is ${\sf{mgh}}$

(Where, m denotes mass , g denotes acceleration due to gravity and h denotes height of the body from the surface of the earth)

➟ Kinetic energy = Energy posses by a body due to it's motion is called kinetic energy of the body. If a body of mass is moving with speed then kinetic energy of body is ${\small{\underline{\boxed{\sf{\dfrac{1}{2}mv^{2}}}}}}$

(Where, m denotes mass and v denotes speed)

Relation between momentum and the kinetic energy is mentioned:

${\small{\underline{\boxed{\sf{K.E \: = \: \dfrac{p^2}{2m}}}}}}$

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➟ Formula to calculate minutes into seconds is mentioned below:

${\small{\underline{\boxed{\sf{1 \: minute \: = 60 \: seconds}}}}}$

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➟ Formula to change kilograms into Newton's is mentioned below:

${\small{\underline{\boxed{\sf{1 \: kilograms \: = 10 \: Newton}}}}}$

${\bigstar \:{\pmb{\sf{\underline{Full \: Solution...}}}}}$

~ Firstly let us convert minute into seconds by using suitable formula!

$:\implies \sf 1 \: minute \: = 60 \: seconds \\ \\ :\implies \sf 5 \: minutes \: = 5 \times 60 \\ \\ :\implies \sf 5 \: minutes \: = 300 \: seconds$

~ Now let us convert kilograms into newton by using suitable formula!

$:\implies \sf 1 \: kilograms \: = 10 \: Newton \\ \\ :\implies \sf 50 \: kilograms \: = 50 \times 10 \\ \\ :\implies \sf 50 \: kilograms \: = 500 \: Newton$

~ Now let us use formula to find out power that is w/t but let us substitute value of w as mgh and let's put the values!

Point to be noted! We can take value of g as 10 m/s² or 9.8 m/s² both or may vary to your question! But let's use g as 10 m/s²

$:\implies \sf p = \dfrac{w}{t} \\ \\ :\implies \sf p = \dfrac{mgh}{t} \\ \\ :\implies \sf p = \dfrac{500 \times 10 \times 30}{300} \\ \\ :\implies \sf p = \dfrac{500 \times 30}{300} \\ \\ :\implies \sf p = \dfrac{15000}{300} \\ \\ :\implies \sf p = \dfrac{150}{3} \\ \\ :\implies \sf p = 50 \\ \\ :\implies \sf Power \: = 50 \: Joules$