Math 10C (Overholser)
Quiz 3
Oct. 29, 2010
Name:
TA:
Section # or Time:
Instructions: You may use a calculator but must show all steps needed to derive your answer. Answers
with no work shown will receive no credit. No simplification of solutions is required for full credit: you may
leave expressions such as sin(4) or
1
√
2
as they are.
1. (5 points) A helicopter is flying at an airspeed of 400 km/hr. A cross wind is blowing
from
the southeast
at 30 km/hr. What direction should the helicopter head to
end up
going directly south? You may find
it helpful to recall that a unit vector at an angle of
θ
from the xaxis is given by cos
θ
~
i
+ sin
θ
~
j
. You may
give your answer in terms of either an angle or a unit vector pointed in the appropriate direction.
Solution:
Let
~w
be the velocity vector of the wind. Since the wind is going towards the northwest, an angle
of 135
◦
from the xaxis, at 30 km/hr,
~w
= 30 cos 135
◦
~
i
+ 30 sin 135
◦
~
j
.
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 Spring '10
 rosanna
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