Question

Three kids are tugging at a blanket with the following forces: 75N [E20ºN], 30N [W] and
100N [S30ºE]. Could you please help me find the magnitude of the net force on the blanket and direction in which its moving.

Thank you.

Answer 1

The net force

$$\bf F=F_1+F_2+F_3.$$

In projections on the axes

$$F_x=F_1 \sin20\degree-F_2+F_3 \cos30\degree\\ F_y=F_1 \cos20\degree+0-F_3 \sin30\degree$$

Hence

$$F_x=75 \sin20\degree-30+100 \cos30\degree=82.3 N,\\ F_y=75 \cos20\degree-100 \sin30\degree=20.5 N.$$

The magnitude of a net force

$$F=\sqrt{F_x^2+F_y^2}=\sqrt{82.3^2+20.5^2}=84.8 N.$$

The direction angle

$$\theta =\tan^{-1}\frac{F_y}{F_x }=\tan^{-1}\frac{20.5}{82.3}=14\degree.$$

Answer: $84.8\rm N[N14\degree E].$