A car travels 6km towards north at an angle of 45o to the east and them travels distance of 4km towa

Question

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

Accepted Answer

(Net distance travellel along x-direction,)
S_x = 6cos 45^o -4 cos 45^o
2 × = √2 km
Net distance travelled along y-direction
S_y = 6 sin 45^o - 4 sin 45^o
10 × = 5√2 km
∴ Net the travelled from the sstarting point,
S =
=

Angle which the resultant makes with the east direction
tan θ = or θ = tan^-1(5)

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