Prove this equation for projectile motion

Winner123 said:

Homework Statement: An object launched with a speed of vi from a height deltay above the horizontal floor will land a certain horizontal distance deltax from the launch point. the initial speed can be shown to be given by
vi=√(xf-xi)^2g/2(yf-yi)

Winner123 said:

##\dots## but idk how to get rid of the negative

PeroK said:

You need a degree in cryptography to be a homework helper these days. Is this something to do with the Generation Z that I've been hearing about?

kuruman said:

Given that the initial velocity is horizontal, you are asked to show that the initial speed can be written as $$v_i=\sqrt{-\frac{g(x_f-x_i)^2}{2(y_f-y_i)}}.$$ If you have already arrived at this expression, there is no negative sign to get rid of because ##(y_f-y_i)<0.##

haruspex said:

As I posted, the given equation is wrong because it does not have that minus sign, unless your eyes are much better than mine.

kuruman said:

Indeed it does not. In post #4 I show the equation that OP is supposed to show in readable form. We don't know whether the equation as given to OP has or does not have the minus sign. I suspect that OP got the correct equation but posted what is to be shown without it thinking that no minus sign belongs under a radical ever. Then OP did the algebra correctly, ended up with a minus sign and is asking us how to "get rid" of the minus sign.

Convoluted? Perhaps, but this is what happens when it is drilled in one's head that overall negative signs do not belong under radicals. There is an easy way to find out, so let's wait to see what OP has to say.

haruspex said:

The given answer is clearly wrong since ##y_f-y_i## is negative.

PeroK said:

Not if the positive y direction is taken to be downwards.

Winner123 said:

from a height delta y above the horizontal floor