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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?

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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 $v_i$.

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