Answer to Question #140532 in Physics for Raffy

Question

Apply component method in finding the resultant vector of the given vectors below. Show your solution.

Scaling: 1cm : 5m

Vector 1 = 25 m ; W
Vector 2 = 61 m ; 35° N of E
Vector 3 = 92 m ; 49.4° S of E

Resultant Vector =x

Answer 1

According to the following figure:

The coordinates of the vectors will be:

$$\mathbf{v}_1 = (-25,0)\space m\\ \mathbf{v}_2 = (61\cos30\degree ,61\sin30\degree) = (30.5\sqrt2 ,30.5)\space m\\ \mathbf{v}_3 = (92\cos49.4\degree ,-92\sin49.4\degree) \approx (59.87 ,-69.85)\space m\\$$

The resultant vector:

$$\mathbf{x} = \mathbf{v}_1 + \mathbf{v}_2 + \mathbf{v}_3=\\ =(-25+30.5\sqrt2 + 59.87, 0+30.5-69.85) \approx (78,-39.35)\space m$$

Answer. $\mathbf{x} = (78,-39.35)\space m$.