# A motorboat heads due west at 10 m/s. The river has a current that travels south at 6 m/s.

a) what is the resultant velocity?

b) If the river is 200 m wide, how long doe sit take the boat to cross the river?

c) How far downstream is the boat when it reaches the other side?

I have a test on all kinds of problems like this tomorrow morning.

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1. b)
I am going to do b first because it is easy
I assume the river is North to South so west is straight across.
Our velocity component straight across is 10m/s
so time to cross = 200m / 10m/s = 20 seconds

Now c) because we know how long we went at 6 m/s downstream
6*20 = 120 meters downstream

Now finally a, the long one
magnitude of resultant velocity = sqrt (10^2 + 6^2) = sqrt (136) = 11.662 m/s
tan angle below straight across = 6/10
so angle south of west = 30.964 degrees

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2. Okay so when we were learning this, we had to add the components and do sine and cosine. Do i have to do that in this problem? If so, where?

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3. Well, I used tangent instead of sine and cosine but if you wanted to use sine or cos do this
We have the hypotenuse = 11.662
so sine angle = 6/11.662
so angle = sin^-1 .5145
which of course is 30.964 again
or we could use
cosine angle = 10/11.662 = .8575
so angle = cos^-1 .8575
which lo and behold is 30.963 close enough :)

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4. You probably gave me a problem that was too easy because you were already given the west and south components instead of a direction and a speed.

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5. Ah got it. Thank you. So another kind of problem that is confusing me, probably because i'm making it harder than it is, is when forces are acting on a point:

Three forves act on a point concurrently. Forve a is 80N at 220 degrees, force b is 70N at 90 degrees, and forve c is 70N at 0 degrees. Find:

a) resultant force

b) equilibrant force

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