aA man has to go 50m due north,40m due east nad 20m due south to reach a field.(a)what is 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:
Distance :
Distance is the total path covered by the man.
Distance travelled by man=50m+40m+20m=110m
Displacement :
Displacement is the shortest path between source [house] and destination [ field]= AB
See the figure :
Draw Perpendicular BE to AC.
BE=CD=40m
AE=AC-CE=50-20=30
NOW, DISPLACEMENT AB=√AE²+EB²
AB=√30²+40²=50m
Angle with horizontal is given by tanθ=30/40=3/4
θ=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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We know that,
Distance = Total Path covered.
So,
Distance = 50 + 20 + 40
→Distance = 110 m
Now,
Fir, Displacement we will find the side of the triangle.
So,
50 m - 20 m
→30 m
_________________________
As, Displacement can't be negative.
So, Displacement = 50 m
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