This has to do with vectors...I'm wondering if I set up the diagram correctly?
A plane has a speed of 250mph and flies with a bearing of N35degE. The wind is blowing from the west at 25 mph with a heading of due east. What is the actual speed and heading of the plane?
Whoops I forgot to include the diagram...here it is:
i.imgur [dot] com/RRY5pox.png
I would tack on the wind vector to the end of the plane vector at the point P so the final end point is Q
Join Q to the origin O
vector OQ has our required direction and its magnitude represents the actual speed
By simple geometry angle P = 125°
so by the cosine law:
OP^2 = 250^2 + 25^2 - 2(250)(25)cos 125°
= 70294.705..
OP = 265.13
So the actual speed is 265.13 mph
Let the additional angle be Ø
by the sine law:
sinØ/25 = sin 125/265.13
sinØ = .07724
Ø = 4.43°
Ø + 35° = 39.43°
So the heading should be N 39.43° E
Thank you <3 you are a lifesaver!
To solve this vector problem, we need to set up a diagram correctly and apply vector addition.
First, let's draw a diagram representing the given information. Draw a line segment to represent the plane's velocity vector, which has a magnitude of 250 mph and is directed N35°E (35 degrees east of north).
Next, draw a second line segment to represent the wind's velocity vector, which has a magnitude of 25 mph and is directed due east.
To find the actual speed and heading of the plane, we need to consider the resulting velocity vector, which is the sum of the plane's velocity vector and the wind's velocity vector.
Now, let's add the two vectors graphically. Place the tail of the vector representing the wind's velocity on the head of the vector representing the plane's velocity. The resulting vector will be the actual velocity of the plane relative to the ground.
To measure the magnitude of the resulting vector (actual speed of the plane), use a ruler to measure the length of the resulting vector.
To measure the direction of the resulting vector (actual heading of the plane), use a protractor to measure the angle it makes with the north direction (clockwise is considered positive, counterclockwise is negative).
Once you have the measured magnitude and direction, you can determine the actual speed and heading of the plane.