How can I rearrange this for the angle?

  • Thread starter iamBevan
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  • #1
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040e7aedfc5c0a9b37f222e28f99fcdf.png


also - The result I'm getting for d is 18587 - this is when I enter 427 for initial velocity, 45 for theta, and 9.81 for g - is this correct?
 

Answers and Replies

  • #2
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To rearrange, use inverse operations to move things you don't want to the other side -

You're dividing the RHS by g, so multiply both sides by g
You're multiplying the RHS by v^2 so divide both sides by v^2
Then use the inverse sin function
etc.

To see if it's correct, compare the result to some other method for estimating the same thing, or even just your intuition.
 
  • #3
HallsofIvy
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I get 18586- with decimal part .o345...

To solve for [itex]\theta[/itex], "unpeel" what has been done:
[tex]d= \frac{v^2sin(2\theta)}{g}[/tex]
so, multiplying both sides by g,
[tex]dg= v^2 sin(2\theta)[/itex]
dividing both sides by [itex]v^2[/itex],
[tex]\frac{dg}{v^2}= sin(2\theta)[/tex]
Taking the inverse sine (arcsin) of both sides
(be careful- since sine is not one-to-one there is no "true" inverse- there are an infinite number of angles with the same sine- two between 0 and pi/2- and "arcsin" only gives one of them)
[tex]arcsin\left(\frac{dg}{v^2}\right)= 2\theta[/tex]
and, finally, divide both sides by 2:
[tex]\frac{1}{2}arcsin\left(\frac{dg}{v^2}\right)= \theta[/tex]
 
  • #4
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Thanks guys - that was a massive help.
 

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