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Question

A body travels a distance of 3 km towards East, then 4 km towards North and finally 9 km towards East.

(i) What is the total distance traveled?

(ii) What is the resultant displacement?


Solution

(a) Given: A body travels a distance of 3 km towards East, then 4km towards North and finally 9 km towards East.
So, the total distance traveled by the body is the length of the path traversed = AB + BC + CA = (3 + 4 + 9) km = 16 km

Displacement is the shortest path between source and destination.
So, in this case, it is Path OC.

(b) If we see the diagram, as ABCD is a rectangle.
AB = CD  =4 km
BC = AD = 9 km
OD = OA + AD = 3 + 9 = 12 km
Consider right angle triangle ODC,
By Pythagoras theorem,
OC2 = OD2 + CD2 = 122 + 42 = 144 + 16
OC2 = 160 km
OC=square root of 160= 12.65 Km

Hence, displacement is 12.65 Km

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