A spelunker is surveying a cave. she follows a passage 180m straight west, then 210m in adirection 45^0 East of south, and then 280m at 30^0 east of north. after a fourth an measured displacement, she finds herself back where she started. use a scale drawing to determin the magnitude and direction of the fourth displacement?
Answers
Answer:
Approximately, the magnitude is 150 m, the angle South of West is 45°.
b) Compute x- and y-components of each vector representing displacement:
1: x=-180,\\ \space \space \space \space \space y=0.\\ 2: x=210\text{ sin}45°=148,\\ \space \space \space \space \space y=-210\text{ cos}45°=-148.\\ 3: x=280\text{ sin}30°=140,\\ \space \space \space \space \space y=280\text{ cos}30°=242.\\ 4: u=?\\ \space \space \space \space \space v=?1:x=−180,
y=0.
2:x=210 sin45°=148,
y=−210 cos45°=−148.
3:x=280 sin30°=140,
y=280 cos30°=242.
4:u=?
v=?
sine she returned to the initial position, the displacement is 0, or x- and y-components of this vector are 0. These components, on the other hand, are the sum of components of vectors 1, 2, 3, and 4. This will help us find u and v:
Ox:0=-180+148+140+u,\\u=-108,\\ Oy:0=0-148+242+v,\\ v=-94.Ox:0=−180+148+140+u,
u=−108,
Oy:0=0−148+242+v,
v=−94.
The magnitude of vector 4?
m=\sqrt{v^2+u^2}=143\text{ m}.m=
v
2
+u
2
=143 m.
The angle (South of West) is
\theta=\text{atan}\frac{94}{108}=41°.θ=atan
108
94
=41°
Explanation:
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Answer: