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Q.

A car travels 6 km towards north at an angle of 45o to the east and then travels distance of 4 km towards north at an angle of 135o to the east. How far is the point from thestarting point? What angle does the straight line joining its initial and final position makes with the east?

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a

50km and tan−1⁡(5)

b

10km and tan−1⁡(5)

c

52km and tan−1⁡(5)

d

52km and tan−1⁡(5)

answer is C.

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Detailed Solution

Net movement along x-directionSx=(6−4)cos⁡45∘i^=2×12=2kmNet movement along y-directionSy=(6+4)sin⁡45∘j^=10×12=52kmNet movement from starting point|S→|=Sx2+Sy2=(2)2+(52)2=52kmAngle which makes with the east directiontan⁡θ=y -component x -component =522∴θ=tan−1⁡(5)
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