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[Mathhelpneeded445]

I have been given this question for a maths example question which I am struggling on can somome please run through the answer and show me how they got it in simple way many thanks I hope you can help me solve it.

 

[HallsofIvy]

First, although this problem might have been given in a Calculus text it sn't have anything directly to do with "Calculus". It is entirely a "vector arithmetic problem.

Second, in order to be held stable the total forces must be 0: A+ B+ C= 0 which means C= -A- B. Using "north-south" and "east-west" as our basic vector components, we can write A= <-775, 0> and B= <0, -646>. So what is C?

 

[Mathhelpneeded445]

How do I find C

 

[hoosie]

a)
If the system is static what does that tell you about the magnitude of the resultant force.
Let unit vector in West direction be i.
Let unit vector in South direction be j.
Let R represent resultant force on drilling platform.

Draw a vector diagram showing:
Fₐ = force on tug A.
Fᵦ = force on tug B.
F?= force on tug C.

Can you express R in terms of the three forces operating on the platform?

If x is the magnitude of the force on tug A and y is the magnitude of the force on tug B write Fₐ and Fᵦ in vector form.
Now express Fₐ + Fᵦ in vector form and show how to add these two vectors in your diagram.
Can you write F?in vector form?
How does F?relate to Fₐ + Fᵦ in your diagram?

Show what happens when F?is added to Fₐ + Fᵦ.

b)
|Fₐ| = 755 kN
|Fᵦ| = 646 kN

Use Pythagoras Theorem to work out |Fₐ + Fᵦ|.
How does this answer compare with |F?|?
Don’t forget to write your answer to 3 significant figures.

c)
In order for the drilling platform to be moved directly east, Rwould have to be increased in an easterly direction.
Let us look at one way this could be achieved.

Draw a vector diagram showing:
Fₐ andFᵦ and the vector represented byFₐ + Fᵦ = 755i + 646j
|R| = 400 kN direction of R is East
F?so that when we add it to Fₐ + Fᵦ we end up with R.

In the triangle formed by the three vectors write in the angle between R and
Fₐ + Fᵦthen calculate |F?| using the cosine rule. Work out the direction of
F?using the sine rule.

Can you devise a scenario where Fₐ, Fᵦ andF? are all reduced in magnitude and the direction of F? is changed so that |R|= 1190 kN in an easterly direction?