SOLUTION: A force of 100N 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 for

Question 1182677: A force of 100N 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.

-> Is it possible to use phytagorean theorem? I'm having a hard time understanding the problem. Please help..
Found 3 solutions by robertb, ikleyn, Edwin McCravy:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
UPDATE: I have edited the solution to correct the fact that cos(105) is a negative quantity, based on what solution other tutors have given.

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Use the cosine law, which says that,
where is the angle between vectors and , and vector is the one opposite to .
Let , , and , the magnitude of the resultant force.

===>
<===> after simplifying.
===>
Therefore the magnitude of force P is around 50N.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~

Use the parallelogram rule of adding vectors and use the cosine law, which says that

        ,

where is the angle between vectors and ,

and vector is the sum of vectors    and .

In our case,   , , and , the magnitude of the resultant force.

===>

===>      after simplifying.

===>

Therefore, the magnitude of force P is around 50 newtons.             ANSWER

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Solved.

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!

Since it makes a 15^o angle with the vertical, it makes a 75^o angle with the horizontal. Yes, you can use the Pythagorean theorem. I made a mistake somewhere, but don't have time to find it and correct it. Maybe you can find the mistake. horizontal | vertical components | components --------------------------------- |P|cos(75^o) N ||P|sin(75^o) N 100 N | 0 N --------------------------------- |P|(cos(75^o)+100 N | |P|sin(75^o) N ______________________________________________________________ |Resultant| = √(sum of horizontal components)² +(sum of vertical components)² Square both sides Subtract 10000 from both sides. Since Use the quadratic formula: We use the + since the - gives a negative value. That's the magnitude of the force P. The angle it makes with the x-axis is found by Edwin

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