Question

For a 70-lb force, and a 60-lb force, The resultant force is 100lb. Are the forces pulling at right angles to each other? Show work please

Answer 1

hi

Answer 2

this is not at right angle, if they are its supposed to be perfect square
Fr=sqrt(70^2+60^2)=100 but they are not

Answer 3

i can solve the real answer to this prob but the question asked doesnot required it

Answer 4

\[F_1+F_2 = 100 \]
F1 and F2 are vectors.

\[F_1=70i\]
\[F_2 = (60cos\theta)i + (60sin\theta)j\]

\[70i + (60cos\theta)i+(60sin\theta)j = R\]
\[(70 + 60cos\theta)i+(60sin\theta)j = R\]

\[\left| R \right| = \sqrt{(70 + 60cos\theta)^2+(60sin\theta)^2}\]
\[100 = \sqrt{(70 + 60cos\theta)^2+(60sin\theta)^2}\]
\[100^2 = (70 + 60cos\theta)^2+(60sin\theta)^2\]
\[100^2-70^2 = 8400cos\theta + 3600cos^2\theta+3600sin^2\theta\]
\[17/12 = 7/3cos\theta + cos^2\theta+sin^2\theta\]

\[cos^2\theta+sin^2\theta = 1\]
\[17/12 = 7/3cos\theta + 1\]
\[3(17/12 - 1) /7= cos\theta\]
\[\theta = cos^{-1}\left ( 3(17\div12)-1)/7\right )\]
\[\theta=79.71^o\]

there could be some other easier way to solve, or maybe i am totally wrong :P check answer