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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?

Language:
English Language

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,

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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