Question

Help with vectors... What am I doing wrong?
A plane is heading N20deg.W at 500 miles per hour through a wind with a speed of 45 miles per hour blowing in the direction of N35deg.E Find the true speed and direction of the plane. (answers are 527.101 mph and 105.990deg.)
The vectors for the plane and wind that I came up with are u=<500cos110,500sin110> v=<45cos55,45sin55> However, I am not getting the right answer. What am I doing wrong?
Thanks for any help.

Answer 1

\[\Large {P=<500\cos 110,500\sin110>\\W=<45\cos55,45\sin55>\\P+W=<500\cos 110+45\cos 55, 500\sin 110+45\sin55>}\]solve \[\large ||P+W||\] and the angle between the vectors \(\large P+W\) and \(\large W\)

Answer 2

@sirm3d Using those vectors I got u+v= < -145.199, 506.708>
lu+vl=sqrt of (-145.199^2 + 506.708^2)= 485.459mph
but the answer should be 527.101mph
perhaps I made a calc. mistake?

Answer 3

\[||P+W||=\sqrt{500^2+2\cdot 500\cdot 45\cos 55+45^2}=527.10145099\]

Answer 4

How did you get 100deg for the plane vector?

Answer 5

\[\Large |u+v|=\sqrt{(-145.199)^2 + (506.708)^2}=527.101\]
your mistake in your calculation is you did not include the negative sign in the square process

Answer 6

You are completely right! I just plugged the numbers in again with parentheses and got the answer. I am extremely grateful for your patience. Thank you so much for helping me :)
Can you help me with one more thing,,,For the direction of the plane what angle am I solving for?

Answer 7

the angle between P+W and W

Answer 8

in your chosen variables, the angle between u+v and v

Answer 9

the answer is 105.990 deg, how are they getting that big of an angle?

Answer 10

that angle is relative to the positive x-axis, which in this case, is the East direction.
So the plane heading relative to the North direction is N 15.99 W