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AP Physics B 2.2 Newtonian Mechanics 174 Views
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AP® Physics B: Newtonian Mechanics Drill 2, Problem 2. If she is to stay on a course due north, at what angle must she point her plane?
Transcript
- 00:03
Shmoop, there it is... Shmoop, there it is...
- 00:07
Angry with the present she got for Christmas, Little Mary Sue
- 00:10
flies an airplane toward the North Pole in order to give Santa an earful.
- 00:14
Oh no, it's cool... she's got a pilot's license.
- 00:16
Mary Sue's plane flies at a speed of 100 meters per second,
Full Transcript
- 00:20
but there is a strong western-blowing wind of 35 meters per second.
- 00:25
If she is to stay on a course due north, at what angle must she point her plane?
- 00:30
And here are the possible answers...
- 00:39
Vectors! Problems!
- 00:40
With direction and magnitude, oh yeah! Whenever we have to deal w/ a problem with
- 00:45
vectors, we always, 100% of the time definitely for sure... draw a picture.
- 00:51
Mary Sue wants her v net to be north, but there is this pesky crosswind keeping her
- 00:56
from doing that easily. Instead, she has to fly diagonally into the
- 01:01
wind so that she can counteract the sideways movement.
- 01:06
V sub p is the flight path that she will take, and v sub w is the movement the plane will
- 01:12
have that is caused by the wind. When we add these two vectors together, we
- 01:16
want to get a north pointing vector... v sub net.
- 01:21
Now to plug in what we know. V sub p is equal to 100 meters per second,
- 01:25
and the wind, v sub w, is 35. That's... all we know.
- 01:29
But frankly, that's all we need to know. Because of the law of SOH CAH TOA,
- 01:38
we know that the cosine of an angle is equal to the adjacent side divided by the hypotenuse.
- 01:44
In this case, the cosine of theta is equal to v sub w divided by v sub p.
- 01:49
We want to find the angle of Mary Sue's plane, so to isolate theta, we take the arc-cosine
- 01:54
of both sides... to get arc-cosine of v sub w over v sub p.
- 02:01
Plugging in values of v sub p and v sub w, we get theta is equal to the arc-cosine of
- 02:06
35 over 100...
- 02:07
...or answer (A).
- 02:09
Give him a piece of your mind, Mary Sue.
- 02:11
St. Nick has to know who's in charge here.
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