Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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...


    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Trying to fix a simplification issue for a general range formula
  1. Kinetics issues (Replies: 4)