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Trying to fix a simplification issue for a general range formula

  1. Oct 31, 2012 #1
    So I have derived a formula for the range of projectile in a vacuum fired from an arbitrary height h from above the ground as the following...

    R=(vcosθ/g)[vsinθ+sqrt((vsinθ)^2+2gh)]


    Now it seems all well and good, but when I try to play with it by multiplying the RHS by the congugate term over the conjugate term (i.e. multiplying by one), I keep coming up with the 2gh factor on top which if h=0 leads to a discrepancy between the two. Can anyone help reconcile this? Note that all factors in the equation are positive values. I can provide a derivation of this equation later if neccessary, but am late to be somewhere and so I must do it later.
     
  2. jcsd
  3. Oct 31, 2012 #2

    haruspex

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    It's not there's a discrepancy. If you plug in h = 0 you will 0/0, which is indeterminate. So the right thing to do is take the limit as h tends to 0 from above, and that will give you sin(2θ)/g, as before.
     
  4. Oct 31, 2012 #3
    Ok, I see the discontinuity now. I feel horrifically blind now.
     
  5. Oct 31, 2012 #4
    Thank you.
     
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