Pythagorean Theorem in finding the boats resultant displacement vector? Support you answer.
2006-09-12 03:32:59 · 7 answers · asked by cristina c 1 in Science & Mathematics ➔ Earth Sciences & Geology
The second vector, 60 degrees E of N, has two components. The E component is 10 sin 60 = 10 (sqrt 3) / 2 = 5 sqrt 3; and the N component is 10 cos 60 = 10 (1/2) = 5.
You get both of these from the 30-60-90 special angles.
To get the resultant vector, you have to add your two vectors together, component by component. In the E direction, you have 25 + 5 sqrt 3; and in the N direction, you have 5.
Your resultant vector can now be expressed as (25 + 5 sqrt 3)i + 5j = 33.66i + 5j (using i and j components), or, as you asked, you can use the Pythagorean Theorem. If you do it that way, you can either (a) just write X^2 = 33.66^2 + 5^2 = 1133 + 25 = 1158, so the resultant X = sqrt 1158 = 34.
The other way to use Pythagoras is
(b) X^2 = (25 + 5 sqrt 3)^2 + 5^2
X^2 = 625 + 250 sqrt 3 + 25*3 + 25 = 725 + 250 sqrt 3 = 1158
so X = sqrt 1158 = 34.
That tells how to use the Pythagorean Theorem, which is what you asked about. But there's another thing you might want to do.
Vectors have both magnitude and direction. If you use X=34 as magnitude, then you ought to show the direction in degrees. If N is zero degrees and E is 90, then you can get the angle using the relation tan x = (25 + 5 sqrt 3) / 5 = 5 + sqrt 3 = 6.732. From that, you get the angle x = 81.55 degrees, showing the direction of the resultant vector -- just a little bit north of east.
2006-09-12 04:35:44 · answer #1 · answered by bpiguy 7 · 0⤊ 0⤋
YOU do the work. Draw a level straight line 25 units long. Then, take your protractor and find 150' angle from horizontal (because if 90' is north, then 60' beyond, or "east of north" make it 150' total). Now connect to get the remaining side and DO YOUR HOMEWORK (which I've already done most of for you).
p.s. Oh, you'll need to drop a vertical, unless you contact Ravi.
2006-09-12 03:41:20 · answer #2 · answered by Anonymous · 0⤊ 0⤋
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2016-09-30 21:08:27 · answer #3 · answered by Anonymous · 0⤊ 0⤋
No need for Pythogorean therom. This is a straight forward case of vector addion.
Mail me for further details.
RAVI
2006-09-12 03:38:30 · answer #4 · answered by sravi_iyer 1 · 0⤊ 1⤋
No I can't. I know that the boat is out of sight now though.
2006-09-12 03:35:21 · answer #5 · answered by toe poe gee gee oh 5 · 0⤊ 1⤋
if this is a homework problem, then i am not gonna answer it. t is simple and I will answer it, if it is not a homework problem
2006-09-12 03:36:28 · answer #6 · answered by vani3624 3 · 1⤊ 0⤋
that is WAY to complicated for me. but at least i tried to answer it...well not really tried but answered it. can i have ten points pretty please??????? I'm not a math person...I'm in high school and have always failed math!!! lol what grade are you in? or are you an adult??? well anyways, can i have ten points pretty please??? thanks if you do give me ten!!!
2006-09-12 03:36:24 · answer #7 · answered by krista 2 · 1⤊ 1⤋