Someone explain to me why I got this problem right in physics

[yhelothar]

So I was tutoring someone in physics today. I worked this problem out, got an answer, but the answer made no sense at all, but she plugged it into her webassign and shazaam, got full credit.

The problem worked out gives 91.5° for A, 146° for B, and 137° for C. How is it possible that as the displacing vector gets smaller, the angle gets larger? I must've understood displacing vector wrong, but I worked the problem out according to the way I drew it.

 

[pmv]

Awkward to reply without diagrams, and I can't be bothered drawing diagrams.

But it seems logical to me. Two displacements, with an angle between them, leading to one total displacement.

Consider the extreme cases...

If the angle between them were zero, say, the the total displacement would be at its maximum, as the two would simply add to each other, both being in the same direction (move 2cm to the right, then another 2cm to the right = 4cm total displacement)

If the angle between them were 180 degrees, then the total displacement would be at its minimum, as the second displacement would reverse the first (2cm to the right, then 2cm to the left = 0cm total displacement).

Between those two the magnitude of the total displacement would be smaller the larger the angle.

(once the angle exceeds 180 degrees the displacement gets larger again)

I would have drawn your first diagram with V2 starting at the end point of V1 (rather than both starting at the origin), which would surely make the point clearer?

 

[yhelothar]

I think I need the diagram because I'm not quite understanding you.
D:

 

[schneiderguy]

I think I need the diagram because I'm not quite understanding you.

 

[DrPizza]

The problem would be much easier to solve using the law of Cosines:
a²=b²+c²-2bcCos(A)

Rearrange for cos(A):
(b²+c²-a&#178/2bc = cos A

Just plug the numbers in. No "physics" to do; it's just math.
(where a is the resultant & A is the angle between the original two vectors.)

Also, (I didn't work it out) as you pointed out, those answers don't make sense. Just estimating, the first angle seems reasonable. Close to a 3-4-5 right triangle, so I'd have predicted 90 degrees, +/- 10 degrees

 

[sdifox]

I am not sure anyone here can answer why. Only the person who generated the website question and answer can.

 

[Numenorean]

42

 

[pmv]

I don't think I agree with the way you've labelled those angles. The third case has an angle between the two vectors of zero not 180 - both vectors are in the same direction, ergo the angle between them is zero. Surely you are measuring the angle from the wrong side? Assuming the black arrows are the components and the blue is the resultant.

 

[Imp]

Looks like you used the 4.4 as an "x" vector (assume angle is 0 degrees), and broke it down into components relative to that "x".

The angles may be "wrong" because of the C A S T rule? Sine peaks at 90 degrees (sine = 1) and starts at 0 degrees (sine = 0). So 146 degrees is the same as 34 degrees in terms of sine.

 

[schneiderguy]

I don't think I agree with the way you've labelled those angles. The third case has an angle between the two vectors of zero not 180 - both vectors are in the same direction, ergo the angle between them is zero. Surely you are measuring the angle from the wrong side? Assuming the black arrows are the components and the blue is the resultant.

Err, yeah you're right D: it made sense in my head. fixed the picture

 

[yhelothar]

Even in this example, the larger the displacing vector, the larger the angle.

 

[yhelothar]

Looks like you used the 4.4 as an "x" vector (assume angle is 0 degrees), and broke it down into components relative to that "x".

The angles may be "wrong" because of the C A S T rule? Sine peaks at 90 degrees (sine = 1) and starts at 0 degrees (sine = 0). So 146 degrees is the same as 34 degrees in terms of sine.

Yeah I did that. I was surprised the angles came out to be greater than 90.

 

[yhelothar]

The problem would be much easier to solve using the law of Cosines:
a²=b²+c²-2bcCos(A)

Rearrange for cos(A):
(b²+c²-a²)/2bc = cos A

Just plug the numbers in. No "physics" to do; it's just math.
(where a is the resultant & A is the angle between the original two vectors.)

Also, (I didn't work it out) as you pointed out, those answers don't make sense. Just estimating, the first angle seems reasonable. Close to a 3-4-5 right triangle, so I'd have predicted 90 degrees, +/- 10 degrees

This rings a bell in my head from when I took trig. I sure as don't remember it though
But it'd probably help her more if I taught her with physics methods.

 

[Matthiasa]

Physics is just applied math though.

 

[esun]

Makes perfect sense.

Imagine lining up two vectors one after the other, like this (magnitudes don't matter for this conceptual exercise): --->--->

Now, those vectors are in the same direction, so the angle between them is 0. This gives the maximum displacement overall, since the magnitudes just add.

Consider rotating the second vector with respect to the first. As you rotate away from 0, you must necessary reduce the total displacement since you'll be rotating toward the original location. In the extreme case, if you rotate it 180 degrees (to point in the opposite direction, then you will have the least overall displacement.

 

[eldorado99]

This thread is boring to me because everyone who responded with a serious answer is smarter than me.

 

[xSauronx]

This thread is boring to me because everyone who responded with a serious answer is smarter than me.

hmmm...same here, i only had to take intro trig so i didnt even get to the law of cosines

 

[eldorado99]

hmmm...same here, i only had to take intro trig so i didnt even get to the law of cosines

I used to kind of get the OP's diagram type of math but about a year or two after high school it all went out the window.

 

[xSauronx]

I used to kind of get the OP's diagram type of math but about a year or two after high school it all went out the window.

i did intro trig last summer and would be hard pressed to recall most of it
/business statistics is gonna be such a pain in the ass when i get to it

 

[eldorado99]

i did intro trig last summer and would be hard pressed to recall most of it
/business statistics is gonna be such a pain in the ass when i get to it

I think it is the kind of activities that I see in your avatar that made me forget most of trig. Probably you too!

 

[Hacp]

Plug it into a computer. It'll solve the problem in a snap.

 

[TecHNooB]

You're looking at the wrong angle

The angle you're looking at is the one formed by summing the vectors. To find the displacement vector, you have to put the two tails together.

 

[Numenorean]

Why are you tutoring someone if you don't fucking know the subject by the way?

 

[Matthiasa]

Because understanding the subject doesn't matter as long as you get the right answer.

 

[DrPizza]

I took a look at what you did & what you did wrong. Close, but no cigar. There's nothing at all wrong with using the Law of Cosines either. It's perfectly acceptable for the resultant of two vectors. (I'm pretty qualified to teach physics too. )

Anyway, your "formula" that you're using is wrong. The y component works out okay, but that's because the sin of an obtuse angle is the same as the sin of it's supplement. But when you calculate the x-component, you should have a minus sign, not a plus sign. Else, you should note that you're finding the supplement of the actual angle.

And, even with that, your 91.5 has a rounding error. Never round off before the last step. Rather than 1.5 above 90, it should be 1.6 below 90: 88.4 degrees. 88.411140664674396634503818597918 according to my calculator. (Of course, rounded off to the correct number of significant digits, which would be 88 degrees.)

The other answers work out to 38.572650822227776481970894599430

and

50.309788436157518979259113035067

Are you doing this tutoring because it's a friend or something? Are you getting paid for this?? (Scary, since you should know that the law of cosines is perfectly acceptable in physics.) Of course, it takes a little away from an intuitive approach, which is why most people would the method you're using (although, perhaps a slightly different style.) Plus, the way you're approaching the problem is pretty efficient when you're trying to find the resultant of half a dozen vectors. I particularly liked the table you started making, too.

I'll upload a diagram in a couple minutes. BTW, you'd have probably noticed this if you hadn't drawn your angle so close to 90 degrees.