Question

An insect moves on a horizontal floor. It covers a distance of 5m from west to east, 2m from north to south and 2√2 m in west-south direction. The displacement of insect from starting point is (nearly).

(1) 9.8 km in west-south direction

(2) 5 m in north-west direction

(3) 5 m at angle of [\(\frac{\pi}{2}-tan^{-1}(\frac{4}{3})\)] east of south

(4) 5 m at angle of tan^-1 (4/3) north of east

Answer 1

(3) 5 m at angle of [\(\frac{\pi}{2}-tan^{-1}(\frac{4}{3})\)] east of south

Choose a co-ordinate system on the floor with intial position of insect as origin of co-ordinates. The three displacement vectors s₁, s₂ and s₃ are as shown in Fig. (a). Expressing the vectors in terms of their rectangular components we have

The resultant displacement s is

This is shown in Fig. (b). Magnitude of s is