1. ## Basic rearranging

I am currently solving questions preparing for my mechanics exam and I am struggling with the final part of the question I have the following equation

y-yo=Vo*sin(beta)*x^2/Vo*cos(beta)-1/2*g*x^2/Vo^2cos^2(beta)

I need to solve this for Vo any help would be much appreciated

2. I'm sorry but this is ambigious. I'll just put what I think the equation is into proper LaTeX form, and please tell us if this is the right one.

$y - y_0=V_0 \times \sin{(\beta)} \times \frac{x^2}{V_0} \times \cos{(\beta)} - \frac{1}{2} \times g \times \frac{x^2}{V_0^2} \times \cos^2{(\beta)}$

Is this the one ?

3. Sorry your right that is the correct equation could you please point me in the right direction on how to solve for Vo

4. Assuming that is correct the $V_0$ and $\frac{1}{V_0}$ in the first term will cancel leaving
$y- y_0= sin(\beta)cos(\beta)-\frac{1}{2}g\frac{x^2}{V_0^2}cos^2(\beta)$

Subtract $sin(\beta)cos(\beta)$ from both sides:
$y- y_0- sin(\beta)cos(\beta)= -\frac{1}{2}g\frac{x^2}{V_0^2}cos^2(\beta)$

Multiply both sides by $V_0^2$:
$V_0^2(y- y_0- sin(\beta)cos(/beta))= -\frac{1}{2}gx^2cos^2(\beta)$

Divide both sides by $y- y_0- sin(\beta)cos(/beta)$:
$V_0^2= -\frac{gx^2cos^2(\beta)}{2(y- y_0- sin(\beta)cos(\beta)}$

And, finally, take the square root of both sides:
$V_0= \sqrt{-\frac{gx^2cos^2(\beta)}{2(y- y_0- sin(\beta)cos(\beta))}}$

$V_0= \sqrt{\frac{gx^2 cos^2(\beta)}{2(sin(\beta)cos(\beta)- y+ y_0)}}$

5. thankyou this has been very helpful