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Study23
 2 years ago
Stuck for a long time :(..........Please help me with vector addition! Illustration below. I need to find the direction and magnitude of the sum vector. The correct answer is 41.62, 42 degrees from x to y
Study23
 2 years ago
Stuck for a long time :(..........Please help me with vector addition! Illustration below. I need to find the direction and magnitude of the sum vector. The correct answer is 41.62, 42 degrees from x to y

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Study23
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1381109606282:dw (Construct c = a + b)

wolfe8
 2 years ago
Best ResponseYou've already chosen the best response.1I believe you are supposed to add them like this: dw:1381110194843:dw

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1I was trying to use the component method (x and y components)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1What are the magnitudes of the two vectors?

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Oh! I forgot to write that! One second...

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1381111017373:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1\(R_x = A_x + B_x = 5 \cos20 + 5 \cos255 \) \(R_y = A_y + B_y = 5 \sin20 + 5 \sin255 \) \(R = \sqrt{R_x^2 + R_y^2} \) \(\theta = \tan^{1} \dfrac{R_y}{R_x} \)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1An angle of 75 deg down form the negative yaxis is an angle of 255 deg from the positive xaxis. The advantage of using the 255 deg angle is that the sin and cos will automatically be negative numbers since it's in the third quadrant.

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Oh!! Okay That makes sense!

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1@mathstudent55 do you mind If I calculate that out to see if I get the correct answer? I've been half an hour, so please don't leave :)

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Hmmm I get 4.61 for magnitude?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1I got 4.62 magnitude, and 42.5 deg.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1What did you get for Rx and Ry?

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Rx: \(\ 5cos20+5cos255 \) \(\ = \) \(\ 0.13... \) Rx: \(\ 5sin20 + 5sin255 \) \(\ = \) \(\ 0.416 \)

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1\(\ \huge \text{The latter should be } Ry. \)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1This is what I get for the components of the resultant. \(R_x = 5 \cos 20 + 5 \cos 255 = 4.6985 + (1.29409) = 3.4044 \) \(R_y = 5 \sin 20 + 5 \sin 255 = 1.7101 + (4.82963) = 3.11952 \)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1\( R^2 = R_x^2 +R_y^2 \) \( R = \sqrt{(3.4044)^2 + (3.11952)^2} \) \( R = 4.6175 \) \( \theta = \tan^{1}\dfrac{R_y}{R_x} \) \( \theta = \tan^{1} \dfrac{3.11952}{3.4044} \) \(\theta = 42.5^o\)

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Hmmm So perhaps the answer key is incorrect?

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1I hope this not too much, but there is one other problem I am stuck on... this time with vector subtraction. Do you mind helping me with that?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1The new vector is b. Now find x and y components of vector a and vector b. Add the components together and find the magnitude of the resultant. Then use the inverse tangent to find the angle of the resultant. dw:1381113881005:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1381114004562:dw

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, and I would still add the components except add the OPPOSITE of the b components?

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1would x still be cos and y still be sin in this case? I always forget when those are switched

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1\(A_x = 8 \cos 135\) \(A_y = 8 \sin 135 \) \(B_x = 4.5 \cos 240 \) \( B_y = 4.5 \sin 240 \) \(R_x = A_x + B_x = 8 \cos 135 + 4.5 \cos 240 = 7.90685\) \(R_y = A_y + B_y = 8 \sin 135 + 4.5 \sin 240 = 1.75974\)

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Where do the 135 and 240 come from?

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1It's subtraction, so shouldn't it be  4.5cos240?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Let me explain that again.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1381114977171:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1These are the original vectors A and B, ok?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1381115051999:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Instead of A + B, they want A  B, right?

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Mathematically speaking, A + B is the same as A + (B). For example, 4  3 = 4 + (3)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1So in order to perform the subtraction of vectors A  B, we can instead add vectors A and B.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1The first step now is to find what the vector B is.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1If vector \(B = B_x + B_y\), then \(B = ( B_x + B_y) =  B_x + ( B_y)\)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1If B is the vector in the figure below, dw:1381115308130:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1381115353688:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Those are the components of B. Then this is B: dw:1381115399994:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Since vector B goes up to the right, vector B goes down to the left.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Now remember that we need to add vectors A and B to subtract A  B.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1381115515926:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1There you have vector A and vector B. Now we need to add them.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1First, let's translate the angles of the vectors to angles starting at the positive x axis.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1381115630429:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Now we need to add a vector with magnitude 8 at 135 degrees and a vector of magnitude 4.5 at 240 degrees.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Now we get x and y components of both vectors.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1\(A_x = 8 \cos 135 = 5.65685\) \(A_y = 8 \sin 135 = 5.65685\) \(B_x = 4.5 \cos 240 = 2.25\) \(B_y = 4.5 \sin 240 = 3.89711 \)

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Ahhh! That makes more sense!

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Now to find the resultant we add the x components to find the x component of the resultant, and we do the same for the y components.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1\( R_x = A_x + B_x = 5.65685 + (2.25) = 7.90685 \) \(R_y = A_y + B_y = 5.65685 + (3.89711) = 1.75974 \)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1Now that we have the x and y components of the resultant, we can use the Pythagorean theorem to find the magnitude of the resultant. \(R = \sqrt{R_x^2 + R_y^2} \) \(R = 8.1\) We find the angle by using the inverse tangent: \(\theta = \tan^{1} \dfrac{R_y}{R_x} \) \( \theta = \tan^{1} \dfrac{1.75974}{7.90685} \) \(\theta = 12.5^o\)

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1381116568714:dw

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Thank you so much @mathstudent55! You're help is invaluable! I was stuck on these for soooo long, thank you thank you!

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.1You're welcome. BTW, notice how I drew the direction in the last picture. The direction is 12.5 deg up from the negative xaxis, or 167.5 deg measured counterclockwise from the positive xaxis. The answer is 8.1 at 167.5 deg.
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