I have a character who needs to jump to a certain height, I want to calculate his initial vertical velocity so that he can achieve that height. Distances and speeds are in logical pixels per second.(adsbygoogle = window.adsbygoogle || []).push({});

The character's position is stored in a 2D vector \begin{pmatrix} x \\ y\end{pmatrix}, and movement is enacted by adding a velocity vector \begin{pmatrix} vx \\ vy\end{pmatrix} to the position vector at every frame. Gravity, with value \begin{pmatrix} 0 \\ -9.8\end{pmatrix} is added to the velocity vector if the character is not in the air.

At frame n, the vy_n can be expressed as vy_n = vy_(n-1) + Gravity, which gives position at frame n y_n = y_{(n-1)} + (vy_n * Δ) where Δ is delta time (the seconds in between two frames, say 1/60)

So, in order to get the character to height h, what should the initial vy be?

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# Initial Y-Velocity (time unknown) in 2D Game

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