text: # Two forces acting in opposite direction have a resultant of 10 N. If they act at right angles to each other the resultant is 50 N , find the magnitude of each force.
  
  2
  by keishambikashsingha
  
  2015-04-19T10:35:11+05:30
  
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  Let the 2 forces be p1 and p2.
  given:
  p1-p2=10.....(1)
  p1^2 + p2^2=50^2.....(2)
  2 equations 2 unknowns. hence they can be solved.
  2015-04-22T14:56:55+05:30
  
  ### This Is a Certified Answer
  
  Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
  Resultant force when the forces are in opposite direction :
  F₁ - F₂ = 10 N    --- (1)
  
  Resultant force Magnitude  when the forces are at right angles:
  F²  =  F₁² + F₂² + 2 F₁  F₂  Cos 90°
  50²  =  F₁² + F₂²    ---  (2)
  
  F₁² + ( F₁ - 10)²  = 2500
  F₁²  - 10 F₁ - 1200 = 0
  
  F₁ = [ 10 + -  √4900 ] / 2 = 40  or  -30 N
  
  F₂ =  30 N  or  - 40 N
  
  The magnitudes of the two forces are :  30 N and 40 N.