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Sagot :
Answer:
17⁰ north of west
Explanation:
We shall represent forces by vector notations . i will represent unit vector towards east and j will represent unit vector towards north .
Jane: 80 pounds, straight east
F₁ = 80 i
Brittany: 100 pounds, north (90 degrees relative to east)
F₂ = 100 j
Robyn: 80 pounds, southwest (225 degrees relative to east ) or 45⁰ south of west
F₃ = - 80cos 45 i - 80 sin45 j = - 80/√2 x ( i + j )
= - 40√2 ( i + j )
Scott: 100 pounds, northwest (135 degrees relative to east) or 45⁰ west of north .
F₄ = - 100 cos 45 i + 100 sin45 j = 50√2 ( - i + j )
Resultant force
= F₁ + F₂ + F₃ + F₄
F = 80 i + 100 j + - 40√2 ( i + j ) + 50√2 ( - i + j )
F = 80 i - 90√2 i + 110√2 j
80 i - 127.26 i + 114.14 j
F = - 47.26 i + 114.14 j
Direction of force
TanФ = 114.14 / 47.26 = 2.4
Ф = 67⁰
67⁰ north of west .
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