Question

Herbert and Randy is playing a friendly game of Serengeti Squash ball (which is basically football but with catchier name) with his antelope friends Thomas, Fred and Darius. On one play Herbert is tackled simultaneously by all three of his long-horned friends, experiencing the following forces:
Thomas: 600N, E 25 degrees S
Fred: 550N, W 40 degrees S
Darius: 610 N, W 37 degrees N

Find the net force on Herbert.

Answer 1

Let us take west -east line to be x-axis then

Resultant of force applied by Fred and Darius is given by

$F_1=\sqrt{550^2+610^2+2\times550\times610\cos77\degree}\\ \ \ \ \ \ =908.6\ N$

Angle which the resultant will make is $\theta=\tan^{-1}(\frac{550\sin77\degree}{610+550\cos77\degree})=36.14\degree\ towards\ 550\ N force\ wrt. \ 610\ N\ force$

Now angle between this resultant force and force applied by Thomas = $155.86\degree$

Final resultant force = $\sqrt{908.6^2+600^2+2\times908.6\times600\cos155.86\degree}{}$

$332.41\ N\\resultant\ angle=\tan^{-1}\frac{908.6\sin155.86\degree}{600+908.6\cos155.86\degree}$ =$180\degree -tan^{-1}(1.62167)=121.66\degree$

$122.66\degree\ clockwise\ towards\ 908.6\ N\ force\ wrt.\ 600\N\ force$ or we can say that $32.34\degree\ south \ of\ west$