- #1

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## Main Question or Discussion Point

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?

- Thread starter iamBevan
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- #1

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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?

- #2

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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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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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