Question

A child pulls a wagon with a force of 40 lbs. The handle of the wagon makes a angle of 30� with the ground. Express the force vector F in terms i and j.

Answer 1

Answer

$F=(20\sqrt{3}lbs)i+(20lbs)j$

Step-by-step explanation:

We have a force (F) of 40 lbs we must declare in terms of i, j

According to the graph

$F=Fx+Fy\\cos\alpha =\frac{Fx}{F} \\sin\alpha =\frac{Fy}{F}\\Fx=F*cos\alpha*i\\Fy=F*sin\alpha*j \\F=F*cos\alpha*i+F*sin\alpha*j\\F=40lbs*cos(30)i+40lbs*sin(30)j\\F=40lbs*\frac{\sqrt{3}}{2}i+40lbs*\frac{1}{2}j\\ F=(20\sqrt{3}lbs)i+(20lbs)j$

Answer 2

The force F in terms of i and j are expressed as  $F=20\sqrt{3}i+20j$

If any force have inclination with ground then it can be always projected in term of i and j. where i represent force component along x axis and j represent force along y axis.

Since, force of 40 lbs. and The handle of the wagon makes a angle of 30 degree with the ground.

force in x direction = $40cos30=40*\frac{\sqrt{3} }{2}=20\sqrt{3} i$

Force in y direction = $40sin30=40*\frac{1}{2}=20j$

So,     $F=20\sqrt{3}i+20j$

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