How Do You Calculate the Components of a Superhero's Displacement?

[motionman04]

Find the horizontal and vertical components of the d = 140 m displacement of a superhero who flies from the top of a tall building following the path shown in Fig. P3.18 where = 35.0°.

The picture is here http://www.webassign.net/pse/p3-20alt.gif

Not sure of exactly where to start.

 

[faust9]

Start by drawing a triangle and writing what you know on it.

 

[motionman04]

well i was able to get the vertical by 140 cos 35, but as I tried 140 sin 35, the answer turned out to be wrong.

 

[Sirus]

Remember your trigonometry: what does cos 35 equal in this triangle? What does sin 35 equal?

 

[rocky811]

I have a question...do you know what the right answer is...because i think i figured it out...ALSO, I don't know if I'm looking at the problem right...but to me the VERTICAL component (Y) looks to me to be opposite of the angle, which would make the y component 140 sin 35...and the x component is adjacent to the angle, which is 140cos 35

 

[Sirus]

That is what I was getting at, hoping motionman would figure it out on his own.

 

[motionman04]

Well I know that sin = opposite over hypotenuse, and cos = adjacent over hypotenuse, I tried 140 sin 35 but apparently that's wrong

 

[Sirus]

The vertical (y) component should be 140 sin 35, the horizontal (x) component should be 140 cos 35. Make sure your calculator is in degree mode.

 

[motionman04]

yep, its in degree mode, and I get an answer of 80.3007 m, however, its wrong for some reason

 

[CinderBlockFist]

140sin35 = 80.3007, so u are right, what does the answer say in the book?

 

[motionman04]

Well its a problem is on webassign.com, and each time I put in that number, it says it is incorrect

 

[CinderBlockFist]

maybe put negative -80.3007, since it is negative according to the x and y-axis on how the diagram is labeled. Other than that, the only thing i can think of is check your significant digits, and how accurate webassign.com wants ur answeres to be.

 

[motionman04]

Yep, that did the trick, thanks for that one cinderblock

 

[CinderBlockFist]

No problem bro

 

[motionman04]

I've got another problem that's been stumping me, it goes like this:

Instructions for finding a buried treasure include the following: Go 77.0 paces at 245°, turn to 130° and walk 110 paces, then travel 100 paces at 162°. The angles are measured counterclockwise from an axis pointing to the east, the +x direction. Determine the resultant displacement from the starting point.

Now, I've found the x, y components for all three vectors, by doing

77 cos/sin 245, 110 cos/sin 130, 100 cos/sin 162, and after finding the resultant vector for the x, it turned out to be wrong.

 

[Pyrrhus]

I hate this Web applets, if you put too many numbers it will say wrong...

try putting -80.30

 

[Pyrrhus]

I've got another problem that's been stumping me, it goes like this:

Instructions for finding a buried treasure include the following: Go 77.0 paces at 245°, turn to 130° and walk 110 paces, then travel 100 paces at 162°. The angles are measured counterclockwise from an axis pointing to the east, the +x direction. Determine the resultant displacement from the starting point.

Now, I've found the x, y components for all three vectors, by doing

77 cos/sin 245, 110 cos/sin 130, 100 cos/sin 162, and after finding the resultant vector for the x, it turned out to be wrong.

Use the components!

Sum all the X components and the Y components, and you will have the displacement in X component and Y component.

Well other than that, let me try

$$\vec{R} = (R_{x}i + R{y}j) m$$

$$R_{x} = 77cos(245) + 110cos(130) + 100cos(162)$$

$$R_{y} = 77sin(245) + 110sin(130) + 100sin(162)$$

$$\vec{R} = (-198.35i + 45.38j) m$$

$$|\vec{R}| = \sqrt{(-198.35)^2 + (45.38)^2} = 203.47 m$$

$$\theta_{R} = 167.11^o$$ Counter-Clockwise.

 

[motionman04]

Yeah, I did, I got the resultant vector for the x components and used that as the displacement vector from the starting point

 

[Pyrrhus]

Yeah, I did, I got the resultant vector for the x components and used that as the displacement vector from the starting point

i don't think that's what is asking. It's asking for the Resultant Vector.

 

[motionman04]

haha no luck with the 221 or 315 degrees,

 

[Pyrrhus]

haha no luck with the 221 or 315 degrees,

That's the answer...

It's a simple polygone shape with one side being the Resultant vector...

 

[Pyrrhus]

Copy me the exact problem with the underlines, so i can see what's expecting...

 

[motionman04]

Well when I added the y resultant, it was -123.148

 

[motionman04]

Wait nevermind, i got 45.38 for the y

 

[Pyrrhus]

Wait nevermind, i got 45.38 for the y

you're correct, i probably put some value wrong in the calculator...

 

[Pyrrhus]

so did the darn thing, finally accepted the answer?