SOLUTION: Can you please check my answer? Our professor has shown us how to get these answers in decimal, and the book shows how to get them with radicals. Question: A child pulls a wagon w

Algebra ->  Trigonometry-basics -> SOLUTION: Can you please check my answer? Our professor has shown us how to get these answers in decimal, and the book shows how to get them with radicals. Question: A child pulls a wagon w      Log On


   

Question 40533This question is from textbook
: Can you please check my answer? Our professor has shown us how to get these answers in decimal, and the book shows how to get them with radicals.
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: 17.32i+10j
Thank You This question is from textbook

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
draw a simple line diagram...basically a right angled triangle. I assume that i is in the horizontal and j is in the vertical directions. Assuming this to be the case, we have the angle 30 degrees and the hypotenuse is 40.

What we are basically doing is "resolving" this into 2 component parts, at right angles to each other:

Horizontally, let this portion/projection of the 40 lb force be called H say, so that using trig:

cos30 = adj/hyp
+sqrt%283%29%2F2+=+H%2F40+
+H+=+20sqrt%283%29+

Vertically, we get an equivalent for the projection, V:

sin30 = opp/hyp
+1%2F2+=+V%2F40+
+V+=+20+

So, the vector of the force pulling the handle can be thought of as +20sqrt%283%29i+ and 20j.

Force is +20sqrt%283%29i+%2B+20j+

Your answer is not correct - from a directional point of view it is fine, but the magnitude of 17.32i + 10j is not 400, it is sqrt%28300%2B100%29 --> sqrt%28400%29 which is 20.

jon.