word problem on Vectors!?
This is the first problem on the sheet I have titled "Vector Applications," and frankly, I am rather lost.
I need some help.
The problem is:
A man pushes a lawn mower with a force of 30 lb exerted at an angle of 30 degrees to the ground. find the horizontal and vertical components of the force.
All I can say is--Say what?
I really want to understand, but I simply do not. It takes me a while to completely grasp a mathematical concept. It also doesn't help that I don't altogether love the more difficult math--pre calc., trig., etc..
That wording is a little odd, but imagine that you have a lawn mower in your hands right now and you're pushing it - the handles of the lawn mower make an angle with the ground (30 degrees).
http://www.zurb.com/me110a/images/pic4.jpg
So the force of 30 pounds is pushed along the handle (at a direction of 30 degrees). Fortunately, that doesn't make the lawn mower move in that direction, or it would go straight into the ground! Instead, there's a horizontal and a vertical component to the force - the vertical component pushes the lawn mower downward while the horizontal component actually makes the lawn mower move forward. So What you have is the following right triangle:
|
|..
|.... 30 pounds
|......
------- <----- 30 degree angle
...x...
So what we need is the horizontal leg of this force diagram. You can find that by setting up a cosine equation:
cos(30˚) = x/30 pounds
I'm not sure if you want exact or not, but cos(30) = Root(3)/2 = .866
.866 = x/30
x = 25.98 pounds
So the horizontal component of the force is 25.98 pounds.
