[tnhoots]

Hello. I'm having trouble with two questions regarding vectors. I'm not asking for solutions-just a step in the right direction.

1)A skater glides along a circular path of radius 4.90m.
a)if he coasta around one half of the circle, find the magnitude of the displacement vector
b)find how far the person skated
c)What is the magnitude of displacement if he skates all the way around the circle

-My first inclination for part a was to find the area of the circle and then multiply that by the degrees of one half the circle (180) and then do the same for c but multiply by (360). I am unsure of b. Is that the right path.


2)Consider two vectors by A=5i-3j and B=-i-2j
a)calculate A+B
b)calculate A-B
c)calculate absolute value of A+B
d)calculate absolute value of A-B

I know the relevant equations are (Ax+Bx)i + (Ay+By)j
However, I don't know how to implement them... suggestions?

[Capuchin]

For 1a) this is testing your understanding of "displacement vector". It is simply the amount and direction the skater has moved from start point to finish point, ignoring any movement in between. The fact he has travelled in a circular motion is irrelevant of where he started and ended up, it's looking for the distance between where he started and ended up.

For 1b) It is asking you for the length of 1/2 the circumference of the circle, this is the actual distance that the skater covered.

For 1c), you need to understand "displacement vector" again. How far has he moved from start to finish ignoring movement in between? (similar to 1a))

2a+b) you need to add I's and j's separately so for a) the answer is (5-1)i + (-3-2)j (can be simplified)

2c+d) you need to find the magnitude of these, I and j are perpendicular, so you can construct a right angled triangle and use pythagoras to find the hypotenuse.

If you need any further elaboration on the above points, please feel free to ask, I tried to give you some good help without spoiling the answers for you, but I can go into more detail if you need.

[tnhoots]

YAY, for the first question, I completed all parts except c. I was thinking that since he skated 9.80m when he went half way around the circle then the magnitude of displacemnt would be 19.6m when he skated all the way around circle. Is that the right way of thinking.
For the second question, I did the addition correctly, however, for the subtraction my answer is (-1-5)i + (-2--3)j when put into the equation B+(-A). This is incorrect. Am I using the wrong equation?

[Capuchin]

You want to use A+(-B), because that's what it says in the question :)

For 1c) you still aren't quite right about what vector of displacement means.
If someone starts at one point, skates in a circle, and ends up back at the same point, how far has he moved from the start?

[tnhoots]

So I would take the absolute value of A+B which was 4i+-5j? I would do that by taking the square root of (4squared + -5squared)? And do the same for the absolute value of A-B which was 6i + -1j? Would I subtract those square roots? I was also trying to find the absolute value by a2 + b2 = c2. And by putting in 2 for a and -3 for b I found the answer to be the square root of 13 which is 3.61. I'm I at least on the right track? And the question also asked about their direction direction would be in degrees from the positive x axis. To do that don't you do tan-1 of y/x??

[Capuchin]

yes the tan^-1 is right I think. You don't need to minus, just use pythagoras' theorem to find the length.

I would do that by taking the square root of (4squared + -5squared)
That's correct, you do the same for A-B

I was also trying to find the absolute value by a2 + b2 = c2
why did you put a=2 and b=-3?? Use the added vectors you have already

Did you work out 1c) yet?