Question

Find the resultant of two forces 130N and 110N respectively. Acting at an angel who's tangent is 12/5.

Answer 1

tanФ=12/5 then cosФ=5/13 (please draw a right angle triangle if you have a doubt) Now √110²+130²+2*110*130*5/13=200N It's whole under root

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Answer 2

The resultant of two forces 130 N and 110 N is 200 N

• The resultant of two vectors acting at an angle is given by

         $R = \sqrt{P^{2} + Q^{2} +2PQcos\alpha }$

• Force is a vector quantity.
• Hence, from the given question we get

         P = 130, Q = 110. tan $\alpha$ = 12/5 ⇒ cos $\alpha$ = 5/13

• Therefore, resultant of the given forces is given by

           $R = \sqrt{130^{2} + 110^{2} +2(130)(110)(5/13) }\\R = \sqrt{16900 + 12100 + 11000 }\\R = \sqrt{40000 }$

           R = 200 N