Question

PLEASE HELP WITH THIS VECTORS PROBLEM!



Explain how you would solve the following problem using rectangular vector components. Your friend swims diagonally across a 25m by 10m pool at 1m/s. How fast would you have to walk around the edges of the pool to get to the same point at the same time as your friend.

Please show all work, thanks :)

Answer 1

just break the velocity into components as we did last time

Answer 2

25/1 and 10/1?

Answer 3

First, find the length of the diagonal and the length of the semiperimeter.
Those are the two distances. You can solve for the time which is the same for both, then solve for the other velocity.

Answer 4

you just need to think about the angle that he is swimming at

Answer 5

so pythagorean theorem?

Answer 6

Hmm, well, if you have to solve it using components (which is needlessly complicated, but good practice) then you might have to break out the sines and cosines..

Answer 7

Please just show me the fastest way

Answer 8

But, yeah, the easy way is to find the diagonal using P.T. and treat it as a simple d=r*t problem, but from the wording, I think it wants you to do it the hard way.

Answer 9

Ive drawn this so far,

Answer 10

Fastest ways is what I said at first: Find the two distances, find the time, then the only unknown in the equation is the second velocity.

Answer 11

Good, draw in the diagonal and use PT to find its length.

Answer 12

So 25^2+10^2=sqrt725=26.93

Answer 13

Right - best to leave it in radical form for now so you don't introduce round-off error too soon.
The swimmer's velocity is 1, so the time to cross in seconds is the same as the distance.
Now find the walker's distance, divide by that amount of time and that is the walker's velocity.

Answer 14

That'll get you a quick answer, but it doesn't really follow the directions given which state to use vector components..
If you'll get points deducted on this assignment for not following directions, then you might have to go ahead and do it the hard way anyway - but at least you'll know what the right answer is ahead of time so you can check your work.

Answer 15

Ok, can we do it the way the question asks then

Answer 16

I assumed you were allowed to have two different velocities around the pool, so I'm not sure I understand the problem.

Answer 17

It asks for the velocity of the walker

Answer 18

one velocity for the horizontal portion, one for the vertical

Answer 19

if it is supposed to be just a single velocity the whole trip I have to rethink it...

Answer 20

wouldnt that just be the avg velocity?

Answer 21

Ultimately, I think you can state the answer as a single constant velocity, but I see no reason why the walker can't change speed after rounding the corner..

Answer 22

You could give the walker vector components of velocity that match the swimmer..
(again, seems needlessly complicated for this problem)
\[v_{swimmer}=(1m/s)(25/\sqrt{725}_{horizontal}+10/\sqrt{725}_{vertical})\]

Answer 23

Ok, for that, I got: 1.3