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

[Numenorean]

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

If you can't explain the how and why, you're worthless to me.

 

[DrPizza]

By the way, that still doesn't explain why your answers are a couple of degrees off for the supplement, unless I made a mistake - it's a pita to use the calculator built into windows.

 

[yhelothar]

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 is okay, 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.

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.

Those answers that in the OP are actually off the top of my head a few hours after I did the problem. We talked about the answers in the whiteboard chat box which I had closed by then. So those answers aren't exact. But my point was that the smaller the angle, the larger the displacement vectors, and my poorly remembered answers was sufficient in showing that.

But I do have the final equation typed out that whiteboard session. You are saying that equation is wrong? I can work out that equation quite easily by using the trig identity sin^2(x)+cos^2(x) =1 and factoring out the 6.5 and get an exact answer. And those answers turned out to be right.

My next guess was actually that I wasn't supposed to be adding the x components but subtracting them. But before I was able to work it out with that idea, she told me she tried the answers and it worked, so I was confused why it was right.

LOL and the headline for my tutoring is actually, An intuitive approach to math and sciences, so yes I'd take the most intuitive approach to doing a problem.

Also I didn't draw the diagram. It isn't a tutor's job to do the problem for the student. I had her draw the diagram, but I didn't want to be pedantic about every little thing. But she actually got confused and thought that was a right angle at one point and was trying to use the pythagorean theorem to find the answer.

But anyways, that forumla I used, apparently is right according to her webassign, even though I thought it was wrong, hence is why I made this thread.

 

[yhelothar]

By the way, that still doesn't explain why your answers are a couple of degrees off for the supplement, unless I made a mistake - it's a pita to use the calculator built into windows.

OK using that angle makes the angle in the diagram makes the answer more sensical. But the problem clearly said the "angle between the two displacements", and there's nothing in between with the angle you chose. :hmm:

 

[DrPizza]

Look at my diagram in the post before your most recent post. It explains very well why your/her answers were wrong.

I've tutored a lot of students in the past. And, I agree completely about not doing their homework for them. Best method: if she couldn't do that problem, or as soon as you saw an error, work out a similar problem with her, with made up numbers. THEN, let her do her homework problem.

One of the most important things in physics is a good diagram. The diagram in the OP was horrible. If that's from the girl you were tutoring, the first thing you should have done was helped her make a better diagram - it would have eliminated the types of mistakes that were made.

 

[yhelothar]

Look at my diagram in the post before your most recent post. It explains very well why your/her answers were wrong.

I've tutored a lot of students in the past. And, I agree completely about not doing their homework for them. Best method: if she couldn't do that problem, or as soon as you saw an error, work out a similar problem with her, with made up numbers. THEN, let her do her homework problem.

One of the most important things in physics is a good diagram. The diagram in the OP was horrible. If that's from the girl you were tutoring, the first thing you should have done was helped her make a better diagram - it would have eliminated the types of mistakes that were made.

So you're saying the answers are actually wrong and that the webassign was wrong also? But we just coincidently got the wrong answers that were the magical right answers?

I'd believe that actually. The answers you worked out subtracing the x component of the 2.5 vector makes more sense. And it's actually considering that we're trying to find the angle "IN BETWEEN" the two displacments.

Thanks for the tips about the diagram. I was really contemplating whether or not to tell her to redo the diagram, but I wanted to try to overlook the smaller things as long as it was sufficient so I'm not nagging about her at everything. I wanted to instill some confidence into her. But you're right about the diagram being very important.