Physics object and forces

Question

For the following object and forces, find a unique equivalent force. specify the magnitude and direction clearly.

Force 1 = 100 newtons going up towards the right at 30deg

force 2 = 160 newtons going up towards the left at 80deg

Answer 1

Possibility 1:

Force 1 = 100 newtons going up towards the right at 30deg to the vertical.

Force 2 = 160 newtons going up towards the left at 80deg to the vertical.

The resultant is:

(100 sin(30) - 160 sin(80), 100 cos(30) + 160 cos(80))

= (- 107.57, 114.39)

Magnitude = sqrt(114.39^2 + 107.57^2)

= 157 at arctan(107.57 / 114.39) = 43.2 deg. to the vertical.

Possibility 2:

Force 1 = 100 newtons going up towards the right at 30deg to the horizontal.

Force 2 = 160 newtons going up towards the left at 80deg to the horizontal.

The resultant is:

(100 cos(30) - 160 cos(80), 100 sin(30) + 160 sin(80))

= (58.82, 207.57)

Magnitude = sqrt(58.82^2 + 207.57^2)

= 216 at arctan(207.57 / 58.52) = 74.2 deg. to the horizontal.