Question 1182677
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A force of 100 N acting horizontally to the right is to be combined with another force P acting upward to the right 
at an angle of 15 degrees with the vertical. If the resultant force of these two forces is 122.83N, solve force P.​
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Use the parallelogram rule of adding vectors and use the cosine law,  which says that


         {{{abs(c)^2 = abs(a)^2 +abs(b)^2 -2*abs(a)*abs(b)*cos(theta)}}},


where  {{{theta}}}  is the angle between vectors  {{{a}}}  and  {{{b}}}, 


and vector  {{{c}}}  is the sum of vectors   {{{a}}}   and  {{{b}}}.



In our case,   {{{abs(c) = 122.83}}},  {{{abs(a) = 100}}},  and  {{{abs(b) = p}}},  the magnitude of the resultant force.


===>   {{{122.83^2 = 100^2 + p^2 - 2*p*100*cos(105^0)}}}


===>   {{{p^2 + 51.76380902p - 5087.2089 = 0}}}   after simplifying.


===>   {{{p = (-51.76380902 + sqrt( 51.76380902^2 -4*1*( -5087.2089)))/2 = (-51.76380902 + 151.7508732)/2 = 49.99347}}}



Therefore, the magnitude of force P is around 50 newtons.   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>ANSWER</U>


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Solved.