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Physics-ASAP

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A plane has an airspeed of 200 {mph}. The pilot wishes to reach a destination 600 {mi} due east, but a wind is blowing at 50 {mph} in the direction 30 degrees north of east.

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 -

    You 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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