# How do I derive this equation?!? HELP!!!

• Sep 13th 2008, 03:54 PM
psychfan29
How do I derive this equation?!? HELP!!!
I started with the equation:
y=yinitial + (vinitialsintheta)t -1/2gt^2

I plugged in t=x/(vinitialcostheta)

to get: y=yinitial + x (tantheta) - [(gx^2)/(2(vinitial^2)(cos^2theta))]

Using derivatives, how do I get from this equation:

y=yinitial + x (tantheta) - [(gx^2)/(2(vinitial^2)(cos^2theta))]

to this equation:

(dy)/(dtheta)=
x(sec^2theta)-[(gx^2(tantheta)(sec^2theta))/(vinitial^2)]

I am completely and totally and utterly confused, bewildered, perplexed, and a list of other things. (Headbang)
Plese help!!!!!
• Sep 13th 2008, 04:31 PM
ticbol
You just have to differentiate the
y=yinitial + x (tantheta) - [(gx^2)/(2(vinitial^2)(cos^2theta))]
with respect to theta.
Then you will arrive at the last line.

Remember that differentiating with respect to theta here means y_initial is constant, and x is constant too.
Of course the g and the V_initial are constants also.

Why not write V_initial as Vo, Y_initial as Yo?