Physics, asked by ravikantverma285, 8 months ago

A man walks 5m towards west and 12m towards north and the 7m vertically upwards. Calculate the magnitudevof sum of their displacement?

Answers

Answered by ExᴏᴛɪᴄExᴘʟᴏʀᴇƦ
9

Answer:

  • A man walks 5 m towars West
  • From there he walks 12 m north
  • Finally he takes a vertical walk of about 7 m
  • Displacement = ?

Diagram

\setlength{\unitlength}{1cm}\begin{picture}(20,15)\linethickness{0.9}\put(8,8){\vector(0,1){1}}\put(8,8){\vector(0,-1){1}}\put(8,8){\vector(1,0){1}}\put(8,8){\vector(-1,0){1}}\put(5,1){\vector(-1,0){3}}\qbezier(2,1)(2,1)(1,1)\put(1,1){\vector(0,1){4}}\qbezier(1,5)(1,5)(1,9)\qbezier(1,9)(1,9)(5,1)\put(2.4,0.5){\sf 5 m}}\put(-0.3,5){\sf 19 m}} \put(0.8,0.5){\sf B}\put(0.8,9.3){\sf A} \put(5,0.5){\sf C}}\end{picture}

\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}

  • So here from the diagram we shall see that the path of the man forms a triangle and so tje shortest distance to reach the final position from the initial position will be the length of the Hypothenuse
  • First we shall find the distance between A & B

\displaystyle\sf\dashrightarrow AB = Distance \ North + Distance \ Vertical\\

  • Vertical = North direction

\displaystyle\sf\dashrightarrow AB = 12+7\\

\displaystyle\sf\dashrightarrow \underline{\boxed{\sf AB = 19 \ m}}

\displaystyle\underline{\bigstar\:\textsf{Displacement of the man :}}

  • The man starts from C and stops at A so as we saw the smallest path to reach A will be the Hypothenuse. We know that ABC is a right angled triangle right angled at B so on using the Pythagoras theorem we shall find the length of AC which will be our Answer!!

\displaystyle\sf:\implies Sum \ of \ the \ side \ square = Hypothenuse^2\\\\

\displaystyle\sf:\implies AB^2+BC^2 = AC^2\\\\

\displaystyle\sf:\implies 19^2+5^2 = AC^2\\\\

\displaystyle\sf:\implies 361+25 = AC^2\\\\

\displaystyle\sf :\implies 386 = AC^2\\\\

\displaystyle\sf :\implies \sqrt{386} = AC\\\\

\displaystyle\sf :\implies \underline{\boxed{\sf AC = 19.7 \ m}}

\displaystyle\therefore\:\underline{\textsf{ The displacement of the man is \textbf{ 19.7 m}}}

⨳ Displacement is a vector quantity that has both magnitude and direction

⨳ Displacement is the shortest path between two lines which is a straight line

⨳ Displacement ≤ Distance

⨳ Distance can never be greater than Displacement

Answered by Anonymous
52

Given:

  • Man walks 5m towards West
  • Then, he walks 12m towards North
  • And then 7m vertically upwards

Find:

  • What will be its Displacement

Solution:

CB = Distance towards North + Distance vertically upwards

CB = 12 + 7

CB = 19m

Now, by using pythogoras theorem

\sf {H}^{2} = {P}^{2} + {B}^{2}

\sf {AC}^{2} = {BC}^{2} + {BA}^{2}

where,

  • BC = 19m
  • AB = 5m

So,

\sf {AC}^{2} = {BC}^{2} + {BA}^{2}

\sf {AC}^{2} = {19}^{2} + {5}^{2}

\sf {AC}^{2} = 361 + 25

\sf {AC}^{2} = 386

\sf AC = \sqrt{386}

\sf AC = 19.646(approx.)

\sf AC = 19.6m

______________________

Therefore, Displacement = 19.6m

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