Answer:
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.
