AP Physics B 2.2 Newtonian Mechanics
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?
|AP Physics B||Newtonian Mechanics|
|AP Physics B/C||Newtonian Mechanics|
|AP Physics C||Newtonian Mechanics|
but there is a strong western-blowing wind of 35 meters per second.
If she is to stay on a course due north, at what angle must she point her plane?
And here are the possible answers...
With direction and magnitude, oh yeah! Whenever we have to deal w/ a problem with
vectors, we always, 100% of the time definitely for sure... draw a picture.
Mary Sue wants her v net to be north, but there is this pesky crosswind keeping her
from doing that easily. Instead, she has to fly diagonally into the
wind so that she can counteract the sideways movement.
V sub p is the flight path that she will take, and v sub w is the movement the plane will
have that is caused by the wind. When we add these two vectors together, we
want to get a north pointing vector... v sub net.
Now to plug in what we know. V sub p is equal to 100 meters per second,
and the wind, v sub w, is 35. That's... all we know.
But frankly, that's all we need to know. Because of the law of SOH CAH TOA,
we know that the cosine of an angle is equal to the adjacent side divided by the hypotenuse.
In this case, the cosine of theta is equal to v sub w divided by v sub p.
We want to find the angle of Mary Sue's plane, so to isolate theta, we take the arc-cosine
of both sides... to get arc-cosine of v sub w over v sub p.
Plugging in values of v sub p and v sub w, we get theta is equal to the arc-cosine of
35 over 100...
...or answer (A).
Give him a piece of your mind, Mary Sue.
St. Nick has to know who's in charge here.