Question

A child pulls a wagon with a force of 40 pounds. the handle of the wagon makes an angle of 30 degrees with the ground. express the force in vector F in terms of i and j.... help please ??!

Answer 1

i and j is a fancy way of saying "break it down into the x and y components".
So if we draw it out, we get:
triangl

In 2D, i is a unit vector that has the value (1, 0). Likewise, j has the value (1,0). If we base this picture on the standard 2D plane, our x unit vector is going right, which means we are going 1 unit in the positive x direction, so we multiply the x value of our force by +i (aka i). However, our y vector is going down, so we multiply the y value of our force by -j, since we are going straight down.

In short:
+i means go right 1 unit
-i means go left 1 unit
+j means go up 1 unit
-j means go down 1 unit

Using trig, we can get the value of the x and y values of the force.
the x part: 40cos30
the y part: 40sin30

As said above, we multiply the x part with i, so we get (40cos30)i as the x component. For the y component, we multiply by -j, so we get -(40sin30)j

Answer 2

thank you sooo much ! this is very helpful (: