Drawing Relative Velocity/Triangle Diagrams?

[kmizzle]

Homework Statement

A balloon with person A in it has a force of gravity of 3000N acting on it. The balloon has an upward force of 3800N due to the hot air in it. Two people are keeping the balloon hovering just above their heads by holding onto ropes attached to each side of the balloon. If person B exerts a force of 540N[Left40°Down] and person C can exert a force of 700N, what is the minimum angle, measured from the horizontal, at which person C should hold the rope in order for the balloon to not fly away?

Homework Equations

The Attempt at a Solution

What I did was:
540sin40=347.12N
Knowing that Fnet"y" should be 0 I did 3800=3347.12N+x
x=452N (person C's horizontal force)

Then this is where I don't know how to solve the problem.

I drew out the relative velocity type triangle diagram by drawing the x component first and then the y component. This would've given me Θ=cos-1(452.88/700)=50°
However, the correct answer is 40°. I didn't know why this was for a long time, but I realized I had to draw the y component and then the x component. This would've given me Θ=sin-1(452.88/700)=40°

So my question is, how do you know whether to draw the x component first or the y component? For previous questions I did I got the correct answer by drawing the x component first, so what makes this one different? :S Thanks!

 

[Averki]

Why did you find 540sin(40)? Where did that 40 come from?

 

[kmizzle]

Why did you find 540sin(40)? Where did that 40 come from?

I did this to find the y component of Person B. 540N was the force, 40 was the angle, and it is sin because it is the y component.

 

[cepheid]

Your question doesn't make any sense to me. It makes no difference in which order you draw the components, as long as you figure them out correctly.

 

[Averki]

I did this to find the y component of Person B. 540N was the force, 40 was the angle, and it is sin because it is the y component.

Was the 40 degrees given in the problem statement?

 

[kmizzle]

Was the 40 degrees given in the problem statement?

Yes, it was stated that Person B was exerting a force of 540N[Left40°Down].

 

[cepheid]

Was the 40 degrees given in the problem statement?

It's right there in the original post!

Homework Statement

A balloon with person A in it has a force of gravity of 3000N acting on it. The balloon has an upward force of 3800N due to the hot air in it. Two people are keeping the balloon hovering just above their heads by holding onto ropes attached to each side of the balloon. If person B exerts a force of 540N[Left40°Down] and person C can exert a force of 700N, what is the minimum angle, measured from the horizontal, at which person C should hold the rope in order for the balloon to not fly away?

kmizzle,

I suspect what's tripping you up is WHEN to use sine and when to use cosine, for x and y components. You have to be careful, because it depends on whether your angle is measured from the horizontal or from the vertical. If the angle is measured from the vertical, then the y-component is given by cosine, and the x-component is given by sine. If the angle is measured from the horizontal, then the y-component is given by sine, and the x-component is given by cosine.

If you always just draw the triangle properly and remember the actual defintion of sine and cosine (sine = opposite side/hypotenuse, cosine = adjacent side/hypotenuse), you'll never get it wrong.

 

[kmizzle]

To clear things up, basically, how do I know the first one is how I'm supposed to draw the diagram with regards to the question? What part of the question tells me that I have to draw the y component and then the x?

 

[Averki]

It's right there in the original post!

Haha... I'm using the PF app and it didn't show up for me... I'm sorry for the confusion.

 

[kmizzle]

It's right there in the original post!



kmizzle,

I suspect what's tripping you up is WHEN to use sine and when to use cosine, for x and y components. You have to be careful, because it depends on whether your angle is measured from the horizontal or from the vertical. If the angle is measured from the vertical, then the y-component is given by cosine, and the x-component is given by sine. If the angle is measured from the horizontal, then the y-component is given by sine, and the x-component is given by cosine.

If you always just draw the triangle properly and remember the actual defintion of sine and cosine (sine = opposite side/hypotenuse, cosine = adjacent side/hypotenuse), you'll never get it wrong.

Ok thanks, I think I have it figured out!

 

[Averki]

To clear things up, basically, how do I know the first one is how I'm supposed to draw the diagram with regards to the question? What part of the question tells me that I have to draw the y component and then the x?

If you look back at the initial problem statement, it asks for the minimum angle measured from the horizontal, not the vertical. Technically, the second triangle in your image is the correct diagram. However, by using the cosine you are finding the x-component of the 700N force, which is not useful in answering this question. If you follow cepheid's advice, which trigonometric function will give you the y-component of the 700N force?

 

[kmizzle]

If you look back at the initial problem statement, it asks for the minimum angle measured from the horizontal, not the vertical. Technically, the second triangle in your image is the correct diagram. However, by using the cosine you are finding the x-component of the 700N force, which is not useful in answering this question. If you follow cepheid's advice, which trigonometric function will give you the y-component of the 700N force?

Yes I see that I need to use sin now and the reason for it! Thank you so much!