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A man travels a distance of 1.5 m toward...

A man travels a distance of 1.5 m towards East, then 2.0 m towards South and finally 4.5 m towards north.
(i) Calculate the total distance travelled.
(ii) Calculate the resultant displacement.

Text Solution

Verified by Experts

The man starts from A and travels `1.5 m` towards east and reaches point B.
For B 2m towards south reaches point C.
From `C 4.5 m` towards north and teaches point D.
Total distance travelled
`= AB + BC +CD`
`= (1.5 + 2 + 4.5) m = 8m `
The resultant displacement is AD. In right angled `Delta ABD, AB = 1.5 m.`
`BD=DC - BC = (4.5 -2) = 2.5 m.`
By Pythogoras. theorem,
`AD ^(2) = AB^(2) + BD^(2)`
` = (1.5) ^(2) + (2.5) ^(2) = 2.25 + 6.25 = 8.50`
` therefore AD = sqrt (8.50) ~~2.92 m`
(i) Total distance travelled `= 8m.`
(ii) The resultant displacement `= 2.92 m.`
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