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.

Explanation:

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.

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explanation:

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