What work have you done so far?
I am not sure how to solve this problem, can someone please help me.
A plane is supposed to travel 820km on a bearing of 80 degrees. The plane's speed is 800km/h. The wind is blowing at 70km/h on a bearing of 100 degrees. What heading should the plane take and how long will the trip take?
This is what I have done so far (the arrows are meant to be on top of the letter to indicate a vector):
Let ->V be the wind
Let ->U be the plane’s speed
Let ->W be the plane’s heading
Vx = 70cos10°
Vy = 70sin10°
Ux = 800cosθ
Uy = 800sinθ
but I don't know how to find the resultant vector without theta.
That is what I meant.
I dont know the desired resultant vector, only the total distance not the speed. I need to find the resultant vector of the 800km/h speed and the 70km/h wind, but I don't know how to do this since i dont know the angle of the speed, I only know the angle of the resultant vector which is 10 degrees.
Addition does not distribute over division. Your second step is therefore incorrect. You've got:
800 sin(θ) + 70 sin(10)
--------------------------- = tan(10),
800 cos(θ) + 70 cos(10)
Now you must multiply both sides by the denominator of the LHS:
800 sin(θ) + 70 sin(10) = tan(10) (800 cos(θ) + 70 cos(10)).
Get all the terms with θ over to the LHS, and all terms without θ over to the RHS.
One recommendation: don't substitute in numbers for anything until the very end. Why? Professors love to give you similar problems with slightly different initial conditions. If you've algebraically solved for the answer, you can just plug those new conditions in to your final answer. If you've plugged in numbers too early, you'll have to re-do everything. It's more work!