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Math Help - vectors velocity

  1. #1
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    vectors velocity

    an airplane is headed north with a constant velocity of 450km/h. the plane encounters a wind from the west at 100 km/h.

    a) in 3h, how far will the plane travel?
    b) in what direction will the plane travel?
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    Quote Originally Posted by william View Post
    an airplane is headed north with a constant velocity of 450km/h. the plane encounters a wind from the west at 100 km/h.

    a) in 3h, how far will the plane travel?
    b) in what direction will the plane travel?
    In one hour the plane will travel \sqrt{450^2+100^2} therefore in three hours it will cover 3\sqrt{450^2+100^2} km

    b) arctan \left(\frac{450}{100}\right)
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    Quote Originally Posted by e^(i*pi) View Post
    In one hour the plane will travel \sqrt{450^2+100^2} therefore in three hours it will cover 3\sqrt{450^2+100^2} km

    b) arctan \left(\frac{450}{100}\right)
    i understand a, it makes sense but can you elaborate a bit more on b? the book gives the answer at 12.5^o east of north
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    Quote Originally Posted by william View Post
    i understand a, it makes sense but can you elaborate a bit more on b? the book gives the answer at 12.5^o east of north
    I should point out that there I made a mistake, that is the angle the plane makes with the horizontal so the actual angle is 90 - \arctan(4.5).

    When I drew my diagram I put the plane at the origin and drew a horizontal line right to represent the wind (100) and a vertical line up to represent the plane going north (450)

    I then made a right-angled triangle from these lines with an angle \theta between them. Part a is asking for the hypotenuse which is Pythagoras' as you got.

    Part b is one of the trig ratios, since the opposite and the adjacent are known directly I used tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{450}{100} = 4.5.

    However, this is the angle is makes with East (as I forgot in my last post), to find the answer from North we need to take this angle from 90.

    90 - \arctan (4.5) = 12.5
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