<li>You are given a vector in the xy plane that has a magnitude of 90.0 units and a y component of -55.0 units.</li>
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<p>(a) What are the two possibilities for its x component?</p>
<p>(b) Assuming the x component is known to be positive, specify the vector which, if you add it to the original one, would give a resultant vector that is 80.0 units long and points entirely in the -x direction.</p>
<p>Does anyone have any ideas?</p>
<p>Please help me. Someone must know.</p>
<p>26 views and no posts?</p>
<p>(a) magnitude^2 = y^2 + x^2
90^2 = (-55)^2 + x^2
8100 = 3025 + x^2
x^2 = 5075
x is about 71. 24 or -71.24 (draw it on a coordinate plane; y is down, so x could go either down and left or down and right)</p>
<p>(b) The original vector has a magnitude 90, and, using cosine, is at about 308 (or -52) degrees. You have to add a vector to create a resultant vector that is 80 units along the x axis going left. Draw a diagram and label the following: the original vector (down&right by 52 degrees compared to the right x axis), a desired resultant vector on the left x-axis, and the line that needs to connect the two.</p>
<p>The angle in the middle is 180-52 = 128.67 (unrounded 52). The two sides of the triangle are 80 and 90. Use the law of cosines to find the length of the desired vector: (the one you create)^2 = original^2 plus (resultant -x vector)^2 - (original)(resultant)cos(middle angle).</p>
<p>r^2 = 90^2 + 80^2 - (90)(80)cos(128.67) = about 138 units. Use law of sines to figure out the angle (the one connecting the original 90 plus your 138 one): sin(128.67)/138 = sinx/80
.45 = sinx
x = about 26.9 degrees (round to 27 to be safe). Now this 27 is not the final answer, because it's actually 52-27 = 25 degrees parallel to the x axis. Plus, it's in the second quadrant, so you subtract it from 180 to get 155 degrees.</p>
<p>Final answer: 138 units at 155 degrees.</p>
<p>Check it at <a href="http://www.1728.com/vectors.htm%5B/url%5D">http://www.1728.com/vectors.htm</a>. The resultant is really close to 80 at 180 degrees.</p>
<p>^^^ that's easier. :)</p>
<p>Is my computer acting up? Someone had an easier way above me, adding the x and y components needed, but they disappeared from my screen :confused:</p>
<p>My method looks flawed, so I deleted it. I presume you are talking about your post and not mine, tkm256.</p>
<p>Dang. I loathe technology. Screw the TI-89s. No, I meant your post. It should work, too, let me check...</p>
<p>I'll repost it, lol...</p>
<p>Basically, original vector's x and y components are 71.2x, -55y, no? If you add a vector w/ components of -151.2x, +55y, you get -80x, 0y. This is assuming that "entirely in the -x direction" means that they want a 0 y component to exist in the resultant vector. This is how my honors physics teacher taught vectors to us last year, and it just seemed to make the process of finding resultants so much easier.</p>
<p>Hm. I got 160 at 20 degrees, which didn't work when I added it to the original. Did you get a different answer?</p>
<p>I know this is not on topic of the post but I was wondering which class is harder ap physics or ap chem??</p>
<p>I thought the method was to just construct a brief table of x and y components, and do simple addition/subtraction to get the desired resultant. If this were a more complex resultant, then you'd go to tan^-1(y/x), etc.</p>
<p>This is my 3rd day in AP Physics class and I don't really understand what part (b) means. But anyway, 138 units at 155 degrees is correct right?</p>