Find the sum of the given vectors displaystyle{700}{N}angle{320}^{circ}+{400}{N}angle{20}^{circ} Rx = ? Ry = ? R = ? theta = ?

djeljenike 2021-02-06 Answered
Find the sum of the given vectors
700N320+400N20
Rx=?
Ry=?
R=?
θ=?
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Expert Answer

Jozlyn
Answered 2021-02-07 Author has 85 answers

Step 1
image
The given expression is,
700N230+400N20
The angle of vector is measured whith positive x-asis.
Step 2
For 700 N, the angle made with positive x-axis is 230
Then angle made by 700 N with negative x-axis is 50
On resolving the vector, we get
f1=700N[(cos(50))i^+(sin(50))j^]
=(697.34N)i^(536.23N)j
For 400 N, on resolving we get
F2=400N[(cos(20))i^+(sin(20))j^]
=(375.88N)i^+(136.81N)j^
Step 3
R=F1+F2
=[(697.34N)i^(536.23N)j^]+[(375.88N)i^+(136.81N)i^+(136.81N)j^]
=[(697.34+375.88)N]i^+[(536.23+136.81)N]j^
=(321.46N)i^+(399.42N)j^
Hence,
Rx=321
Ry=399
R=Rx2+Ry2
=(321)2+(399)2
=513
Step 4
image
tanα=|Ry||Rx|
α=tan1,|Ry||Rx|
=tan1(399.42321.46)
=51
Then angle made by resultant vector with positive x-axis is,
θ=180+α
=180+51.17

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