Multiple Concept Example 9 deals with the concepts that are important in this problem. A grasshopper makes four jumps. The displacement vectors are (1) 40.0 cm, due west; (2) 26.0 cm, 32.0 ° south of west; (3) 19.0 cm, 50.0 ° south of east; and (4) 18.0 cm, 60.0 ° north of east. Find (a) the magnitude and (b) direction of the resultant displacement. Express the direction as a positive angle with respect to due west.

We shall convert the movement of grasshopper in vector form. Suppose the grass hopper is initially sitting at the origin or (00) position.

It went 40 cm due west so

D₁ = - 40 i

It then moves 26 cm 32 ° south of west so

D₂ = - 26 Cos32i - 26 Sin32 j = - 22 i - 13.77 j

Then it moves 19 cm 50° south of east

D₃ = 19 Cos 50 i - 19 Sin 50 j = 12.2 i - 14.55 j

Then it moves 18 cm 60° north of east

D₄ = 18 Cos 60 i + 18 Sin 60 j = 9 i + 15.58 j

Total displacement = D₁ + D₂+D₃+D₄

= - 40i - 22 i - 13.77 j + 12.2 i - 14.55 j + 9 i + 15.58 j

= - 40.8 i - 12.74 j

Magnitude of displacement D

D² = (40.8) ² + (12.74) ²

D = 42.74 cm

If ∅ be the required angle

Tan∅ = 12.74 / 40.80 =.31

∅ = 17 ° positive angle with respect to due west.