Planes rarely fly in the direction they are pointing.
If the wind is blowing and the world is turning the pilot has to take
account of these when he plots a course. Even with modern gps systems
available, , it is beneficial to the pilot to take these into account
because of the resulting increase in fuel efficiency. It is worse
though for the sailor, who has to take the tide into account as well
We can deal with these problems by representing the
velocities of the wind, tide and boat as vectors, then using
trigonometry to find the course to take or the velocity to travel at.
For example:
A motor boat travels in a straight line across a river which flows
at 3m/s between straight parallel banks 200 m apart. The motor boat,
which has a top speed of 6m/s in still water, travels directly from a
point A on one bank to a point B, 150m downstream of A, on the
opposite bank. Assuming that the motor boat is travelling at top
speed, find, to the nearest second, the time it takes to travel from
A to B.
What is the first thing you do? DRAW A DIAGRAM!!
The
river is flowing downstream to the right at 3m/s. We don't know the
direction in which the boat will steer but we do know the bearing of
B from the start point is 36.87 hence the angle BA makes with the
horizontal is
We
can draw the following diagram:
Then
Now use the cosine rule to find
Then the time to reach B is
No comments:
Post a Comment