EXTRA EXAMPLES
Example 1
The diagram below shows the forces acting on a plane which is flying at a constant
height.
There is a large force of 400,000 newtons
from the engine thrust and a
smaller force of 40,000 newtons from the wind.
[ The lift generated the air flowing
over the wings exactly balances the downward force of gravity on the plane so we do
not need to consider vertical forces here ].
To begin with the plane is headed due East.
The
diagram below is a 2D diagram
drawn from the point of view of someone looking down on the plane.
(a)
Use vector methods to find the total force vector acing on the plane
(express your answer in terms of
i
and
j
)
(b)
What direction is the total force pointing in ?
(c)
What direction will the plane actually fly in when we take both forces into
account
(d)
In what direction
θ
(measured from the positive x axis) should the pilot fly
in so that the plane is actually flying due east
?
The wind is still
blowing at an angle of 30 degrees.
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SOLUTION
Be careful here to underline the vectors
i
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 Three '11
 MariaAneiros
 Math, Dot Product, Force, Euclidean vector, total force

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