Question

Two forces while acting on a particle in opposite directions,
have the resultant of 10 N. If they act at right angles to
each other, the resultant is found to be 50 N. Find the two
forces.
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Answer 1

Explanation:

First case :

Resultant 1,

R1 = √(F1^2 + F2^2 + 2F1F2 cos(theta)

F1 - F2 = 10

Second case :

R2 = √(F1^2 + F2^2 + 2F1F2 cos(90°)

F1^2 + F2^2 = 50^2

F2 = 30N

F1 = 40N