- #1
jonroberts74
- 189
- 0
an object is moving in the direction i + j is being acted upon by the force vector 2i + j, express this force as the sum of a force in the direction of motion and a force perpendicular to the direction of motion.
the parallel would be [tex] \hat{i}+\hat{j}[/tex] and the orthogonal would be [tex]\hat{i} - \hat{j}[/tex]using projection of F onto the parallel and orthogonal
[tex] \frac{<1,1>\cdot<2,1>}{||<1,1>||^2}<1,1> = <\frac{3}{2}, \frac{3}{2} >[/tex]
[tex] \frac{<1,-1>\cdot<2,1>}{||<1,-1>||^2}<1,-1> = <\frac{1}{2} , \frac{-1}{2}>[/tex]
[tex] \vec{F} = <\frac{3}{2}, \frac{3}{2} > + <\frac{1}{2}, \frac{-1}{2} > [/tex]
[tex] = 2\hat{i} + 1\hat{j} [/tex]
the parallel would be [tex] \hat{i}+\hat{j}[/tex] and the orthogonal would be [tex]\hat{i} - \hat{j}[/tex]using projection of F onto the parallel and orthogonal
[tex] \frac{<1,1>\cdot<2,1>}{||<1,1>||^2}<1,1> = <\frac{3}{2}, \frac{3}{2} >[/tex]
[tex] \frac{<1,-1>\cdot<2,1>}{||<1,-1>||^2}<1,-1> = <\frac{1}{2} , \frac{-1}{2}>[/tex]
[tex] \vec{F} = <\frac{3}{2}, \frac{3}{2} > + <\frac{1}{2}, \frac{-1}{2} > [/tex]
[tex] = 2\hat{i} + 1\hat{j} [/tex]