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January 25, 2015

January 25, 2015

Posted by **Fizza** on Wednesday, September 28, 2011 at 2:30pm.

a)In what direction must the pilot head the plane in order to reach her destination? answer in south of east

b)How long will the trip take?

answer in hours

can you please show me step by step so i can check my answer?

thanks

- Physics-ASAP -
**Steve**, Wednesday, September 28, 2011 at 3:57pmYou want two vectors which add up to (0,600). The airspeed has length 200t in an unknown direction, angle a. The other has length 50t, in the direction 30º north of east.

So, if the destination D = (600,0)

P is the point where the plane would have ended up with no crosswind.

P = (x,y) where

y = -25t because of the 30º angle.

So, now we have two right triangles.

On the left, the hypotenuse = 200t, height = 25t, base = 25t√63

On the right, hypotenuse=50t, height=25t, base=25t√3

Now, we know that the two bases add up to 600mi.

25t(√63+√3) = 600

t = 2.48 hrs

Using the plane's triangle, sin(a) = 1/8

a = 7.18º south of east.

You can use the law of cosines to verify that the numbers are correct.

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