Question

A man has to go 50 m due north, 40 m due east and 20 m due south to reach a field
(a) What distance he has to walk to reach the field ?
(b) What is his displacement from his house to the field?
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Answer 1

Answer:

Distance :Distance is the total path covered by the man.Distance travelled by man=50m+40m+20m=110mDisplacement : Displacement is the shortest path between source [house] and destination [ field]= ABSee the figure :Draw Perpendicular BE to AC.BE=CD=40mAE=AC-CE=50-20=30NOW, DISPLACEMENT AB=√AE²+EB²AB=√30²+40²=50mAngle with horizontal is given by tanθ=30/40=3/4θ=tan⁻¹[3/4] direction north to east.∴His displacement from his house to field is 50m , tan⁻¹[3/4] direction north to east.

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