Question

4) Two forces acting in the opposite
directions have a resultant of 10 N. IL
they act at the right angles to each
other, the resultant is 50 N. The
magnitudes of the forces are
(1)40 N, 30N (2) 50 N, 40N
(3) 30 N, 20 N (4) 35 N 25 N​

Answer 1

Answer:F1-F2=10 N…………(1)

F1^2+F2^2=2500 N^2. OR

(F1-F2)^2+2F1F2=2500 OR

100+2F1F2=2500 OR

F1F2=1200 N^2 OR

F1=1200/F2. Using this result in equation (1),

(1200/F2)-F2=10 N OR

F2^2+10F2–1200=0 OR

F2^2+40F2–30F2–1200=0 OR

F2(F2+40)-30(F2+40)=0 OR

(F2–30)(F2+40)=0. Therefore ,

F2=30 N and using this value in equation ((1), F1=40N.