A spy report about a suspected car reads as follows. “The car moved 2.00 km towards east, made a perpendicular left turn, ran for 500 m, made a perpendicular right turn, ran for 400 km and stopped”. Find the displacement of the car.

Taking unit vectors in X and Y directions as i and j, the given displacements can be written as, = 2i, =0.5j and =4i


Hence the resultant displacement vector OC = =2i +0.5j+4i =6i+0.5j


Magnitude of the displacement = == 6.02 km


Angle between resultant displacement and east (x-axis) is given by tanθ = (0.5/6) =1/12,


Therefore, θ=tan-1(1/12)


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