HELP ME PLEASE ! (reposted)
(Resolving Vector) A woman pushes a 50-N lawn mower with a force of 25 N. If the handle of the lawn mower is 45 degrees above the horizontal, how much downward force is the lawn mower exerting on the ground? How much force causes the motion of the lawn mower horizontally?(neglect friction)

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- anonymous

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- phi

Did you sketch a picture ?

- anonymous

No, I don't know how to begin it.

- phi

|dw:1382104719667:dw|

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## More answers

- phi

do you see the 25N force along the handle can be broken into sideways and up/down ?
do you see you have a 45-45-90 triangle. You know the hypotenuse.
can you find the length of the (equal) legs ?

- anonymous

No, i can't @phi

- phi

to do this problem you need to know some physics and some math
Let's start with the math
|dw:1382105210794:dw|
can you solve for x ?

- phi

you should get
\[ 2 x^2 = 25^2 \\ x^2 = \frac{25^2}{2} \\
x= \sqrt{\frac{25^2}{2} }= \frac{25}{\sqrt{2}}= \frac{25 \sqrt{2}}{2}
\]

- anonymous

25/sin 90 degrees * x/sin 45 degrees
(25)(sin 45 degrees) = (x)(sin 90 degrees)
i'm not really sure with this yet

- anonymous

why is it 2x^2 = 25^2 ?

- phi

First, using the Law of Sines works. sin 45 = sqr(2)/2 and sin 90 = 1
you get
x= 25 sqr(2)/2 which is good.
I used geometry. you have a right triangle which is also isosceles, so its 2 sides are equal.
You can use pythagorean theorem a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse
\[ x^2 + x^2 = 25^2 \\ 2x^2= 25^2\]

- phi

If the pythagoraean theorem does not ring any bells, you should learn it.

- anonymous

I got the phythagorean theorem, thanks :) Can you still help with the next step on answering it?

- phi

now you have this picture
|dw:1382106175853:dw|

- phi

can you answer the questions?
the sideways force is only the one vector
the downward force is the sum of two vectors

- anonymous

Is the downward force: 25^2/2 and 50 N?

- phi

25^2/2 means 25*25/2
do you mean \( 25 \sqrt{2}/2\) ?

- anonymous

No. What I mean is the 25 sqr(2)/2 and 50 N.

- phi

then yes, you add those two values... the vectors are pointing in the same direction so you can just add their lengths to get the total length of the "resultant vector"

- anonymous

i'm confused with the 25 sqr(2)

- phi

first, it is \[ \frac{25\sqrt{2}}{2} \]
you can add 50 to it like this:
\[ 50+ \frac{25\sqrt{2}}{2} \]
that is an exact answer. you can use a calculator and find a decimal number, but you will have to round the decimal number (because in theory the answer has an infinite number of digits on the right side of the decimal point)
see http://www.wolframalpha.com/input/?i=+100+digits+of+50+%2B+25*sqrt%282%29%2F2

- anonymous

so that would be the answer for the downward force? @phi

- phi

yes

- anonymous

thanks :) how about the force horizontally?

- phi

look at the picture. How big is the vector that goes sideways ?

- anonymous

25 sqr(2)/2 ?

- phi

yes. or as a decimal about 67.678 N

- anonymous

Thank you very much for helping! @phi ^_^

- phi

yw

- phi

oops I just noticed I posted the wrong decimal value for the horizontal force
25* sqrt(2)/2 is about 17.678 N (NOT 67.678 N which is the downward force)

- anonymous

its okay. thanks for reminding :) @phi

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