# Projectile Motion, solving for initial velocity [closed]

I'm stumped on a projectile motion launched from a cliff at an angle. The only known values that are given are the height of the cliff $$h$$, The total horizontal distance covered $$d$$ and the incline of the ramp $$\theta$$ and it asks to find the initial velocity $$v_i$$. How could I approach solving this problem?

I took another stab at it and I was able to solve it using the following equations: $$x_f=x_i+v_xt$$ $$y_f=y_i+v_y{_i}t +\frac 12at^2$$ Applying and rearranging these to my problem For x-direction I get: $$d=0+v_i\cos\theta\cdot t$$ $$v_i=\frac{d}{\cos\theta\cdot t}$$ And for y-direction: $$0=h+v_i\sin\theta\cdot t -\frac 12gt^2$$ Apply previous equation and solve for $$t$$: $$0=h+\frac{d\cdot \sin\theta\cdot t}{\cos\theta\cdot t} -\frac 12gt^2$$ $$0=h+d\cdot \tan\theta -\frac 12gt^2$$ $$\frac 12gt^2=h+d\cdot \tan\theta$$ $$t^2=2\cdot\frac{h+d\cdot \tan\theta}{g}$$ $$t=\sqrt{2\cdot\frac{h+d\cdot \tan\theta}{g}}$$ And finally, value for $$t$$ can be used in the first equation to solve for $$v_i$$.