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# 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

- Al PLv 71 decade agoFavorite 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

- sheldonlinkerLv 61 decade ago
A = 5m @ 25Â°

B = 8m @ 60Â°

The X component of A is 5Â·Cos(25Â°)

The X component of B is 8Â·Cos(60Â°)

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

The Y component of A is 5Â·Sin(25Â°)

The Y component of B is 8Â·Sin(60Â°)

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

The distance of the answer is â(final Y componentÂ² + final X componentÂ²).

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