# Math Help - vector help

1. ## vector help

The angle of POW is 45 . In the diagram OP represents
the velocity of an aircraft cruising at a constant
velocity of 500 km per hour due north . OW represents
the constant wind velocity of 50 km per hour . How
far will the aircraft deviate from its original path after
it has travelled for 3 hours .

P W

O

The angle of POW is 45 . In the diagram OP represents
the velocity of an aircraft cruising at a constant
velocity of 500 km per hour due north . OW represents
the constant wind velocity of 50 km per hour . How
far will the aircraft deviate from its original path after
it has travelled for 3 hours .
...
Use a coordinate system with the x-axis pointing East and the y-axis pointing North.

Then the vector which describes the flight of the air plane in one hour is:

$\vec a=(0, 500)$ and the vector describing the winds movement in one hour is

$\vec w = \dfrac{50}{\sqrt{2}}\cdot (1,1)$

The course over ground of the airplane in t hours is:

$\vec c = t \cdot (\vec a + \vec w )= t \cdot \left(\dfrac{50}{\sqrt{2}}\ ,~ 500+\dfrac{50}{\sqrt{2}} \right)$

The position of the plane after 3 hours flight will be:

$P\left(\dfrac{150}{\sqrt{2}}\ ,~ 1500+\dfrac{150}{\sqrt{2}} \right)$

Without any wind the plane would be at $P_0\left(0\ ,~ 1500 \right)$

Now calculate the difference between these two places.