Posted by Mary on Saturday, April 20, 2013 at 4:50pm.
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?
- Trig - Mary, Saturday, April 20, 2013 at 4:51pm
Whoops I forgot to include the diagram...here it is:
i.imgur [dot] com/RRY5pox.png
- Trig - Reiny, Saturday, April 20, 2013 at 10:02pm
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°
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
- Trig - Mary, Sunday, April 21, 2013 at 12:29pm
Thank you <3 you are a lifesaver!
Answer This Question
More Related Questions
- Trig - A plane has a speed of 250mph and flies with a bearing of N35degE. The ...
- geometry - A plane is heading west at 200 mph. The wind is blowing S30°W at 25 ...
- trig - A plane is flying due south at a speed of 192 mph. a wind is blowing in ...
- Math - Me, again... Please help me. Thank you. Assume a plane is flying directly...
- Geometry/trig - A plane is flying due south at a speed of 300 mph. The wind is ...
- trig - A plane is flying 225 mph heading South 25°West. The wind is blowing ...
- Calculus - An airplane is heading at a bearing of N23°E at a speed of 700 km/hr...
- Geometry - A plane is heading west at 200 mph. The wind is blowing S30°W at 25 ...
- Trig/Precal - An airplane flies on a compass heading of 90° at 310 mph. The wind...
- Trig - An airplane is flying on a compass heading (bearing) of 340 degrees at ...