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.
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.