# Parabolic motion to reach certain point

#### rob555

https://ibb.co/n57i8y

what is the formula to specify the correct v0y and v0x to reach the red point and x max?

#### HallsofIvy

https://ibb.co/n57i8y

what is the formula to specify the correct v0y and v0x to reach the red point and x max?
There are an infinite number of different ways to cover the same parabolic path. If we take the "horizontal speed" to be constant, then we can write $$\displaystyle x= v_{0x}t$$ and $$\displaystyle y= -(g/2)t^2+ v_{0y}t$$. But I see two different "red points". y will be 0 at both t= 0 and $$\displaystyle t= \frac{2v_{0y}}{g}$$. At that point x is $$\displaystyle x_{max}= \frac{2v_{0x}v_{0y}}{g}s$$

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