Solving v^2/2=gs(sin(α)+cos(α)*k): Get k with Steps

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CarrotWilliams
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I've gotten to this point:
v^2/2=gs(sin(α)+cos(α)*k)

I'm suppost to get "k" from this equation can some help by showing me the steps because I'm a bit confused on how to do it.
 
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CarrotWilliams said:
I've gotten to this point:
v^2/2=gs(sin(α)+cos(α)*k)

I'm suppost to get "k" from this equation can some help by showing me the steps because I'm a bit confused on how to do it.
Welcome to the PF.

In your future schoolwork posts here, please fill out the Homework Help Template that you are provided, and show your best efforts to work the problem.

So start off by distributing terms on the righthand side (RHS) -- you should separate the two terms. Then move the first term on the RHS to the LHS with subtraction. Then how do you get k all by itself on the RHS?
 
berkeman said:
Welcome to the PF.

In your future schoolwork posts here, please fill out the Homework Help Template that you are provided, and show your best efforts to work the problem.

So start off by distributing terms on the righthand side (RHS) -- you should separate the two terms. Then move the first term on the RHS to the LHS with subtraction. Then how do you get k all by itself on the RHS?
So I've gotten the result: k= v^2-g*sin(α)*s/2*cos(α)*g*s <----- is this correct ?
 
CarrotWilliams said:
So I've gotten the result: k= v^2-g*sin(α)*s/2*cos(α)*g*s <----- is this correct ?
Could you show each of your steps? That would make it easier to check... :smile:
 
Also, please be careful and explicit with parenthesis when typing the equations out with just text. There is a LaTeX primer under INFO, Help-How-To at the top of the page, BTW. :smile:
 
berkeman said:
Could you show each of your steps? That would make it easier to check... :smile:
  1. v2/2 = g*sin(α)*s + k*cos(α)*g*s
  2. k*cos(α)*g*s = 1/2*v2-g*sin(α)*s
  3. k = v2-g*sin(α)*s / 2*cos(α)*g*s
 
CarrotWilliams said:
  1. v2/2 = g*sin(α)*s + k*cos(α)*g*s
  2. k*cos(α)*g*s = 1/2*v2-g*sin(α)*s
  3. k = v2-g*sin(α)*s / 2*cos(α)*g*s
Looks okay to me, but as I mentioned, it's best to explicity show parenthesis when just typing out equations in text. So I'd modify your last equation to:

k = [ v2-g*sin(α)*s ] / 2*cos(α)*g*s
 
BTW, there are also other ways to express the final RHS, depending on what you want to do with it going forward. For example, you could show it as two separate fractions, with a tan(α) in the 2nd term... :smile:
 
berkeman said:
Looks okay to me, but as I mentioned, it's best to explicity show parenthesis when just typing out equations in text. So I'd modify your last equation to:

k = [ v2-g*sin(α)*s ] / 2*cos(α)*g*s

ok thanks for your help !
 
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CarrotWilliams said:
  1. v2/2 = g*sin(α)*s + k*cos(α)*g*s
  2. k*cos(α)*g*s = 1/2*v2-g*sin(α)*s
  3. k = v2-g*sin(α)*s / 2*cos(α)*g*s
You do need a set of parentheses around the denominator, to remove ambiguity. White space around the division symbol does not change its meaning in the real world, even though some middle high teachers may have misled you otherwise.

So your eqn 3 needs to be written as k = (v2-g*sin(α)*s) / (2*cos(α)*g*s)

For exactly the same reason, I'd like to see your eqn 2 written with parentheses around the 1/2 to emphasise clarity, e.g.,
k*cos(α)*g*s = (1/2)*v2-g*sin(α)*s

But it's still not right. You messed up in going from 2. to 3, probably because of this sloppiness with the solidus sign, where you have it doing one thing in eqn 2 and something different in 3.

Try that step again, starting with your eqn 2.
 
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