If two forces act in opposite direction then their resultant is 10N and if they act mutually perpendicular then their resultant is 50N. Find the magnitudes of both the forces.
If the forces act as in the opposite direction then,
F1−F2=10N...........1
And if they both act as a perpendicular then √F21+F22=50N..............2
From equation 1 we get F1=10+F2 put this value in equation 2 then we get,
(F2+10)2+F22=502
⇒F22+F22+100+2F2=2500
⇒2F22+2F2−2400=0
⇒F22+40F2−30F2−1200=0
⇒F2(F2+40)−30(F2+40)
⇒(F2−30)(F2+40)
⇒F2=30N
Put this value in equation 1 then we get,
F1=10+30=40N