Physics vector question?

vector A = 5 meters at 25 degrees

vector B = 8 meters at 60 degrees

If vectors A + B described a walking path from some arbitrary starting point, how far and in what direction would you have to walk to return to the exact starting point along the shortest path possible?

2 Answers

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  • Al P
    Lv 7
    1 decade ago
    Favorite Answer

    Sum the components:

    Dx:

    5* Cos(25)+ 8* Cos(60) =8.53153893518323 m

    Dy:

    5* Sin(25)+ 8* Sin(60) =9.04129453897902 m

    With rounding:How far:

    Sqrt(Dx^2+Dy^2) = 12.4311 m

    Arctan(Dy/Dx) = 46.66 degrees

    Direction to starting point:

    Angle = 180+46.66 = 226.66 degrees CCW

  • 1 decade ago

    A = 5m @ 25°

    B = 8m @ 60°

    The X component of A is 5·Cos(25°)

    The X component of B is 8·Cos(60°)

    Add the X components together to find the X component of the answer.

    The Y component of A is 5·Sin(25°)

    The Y component of B is 8·Sin(60°)

    Add the Y components together to find the Y component of the answer.

    The distance of the answer is √(final Y component² + final X component²).

    The angle of the answer is Arctan(final Y component/final X component).

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