Vector Addition
In the picture of the skater provided, assume that he has the same amount of vertical and horizontal take-off velocity. These velocities are represented by one vertical and one horizontal arrow originating from the center of mass of the skater.
To calculate the take-off angle and velocity you need to draw the arrow representing the vertical velocity over at the tip of the arrow representing horizontal velocity (just slide it over). Drawing the vertical and horizontal velocity arrows in such a manner is called drawing the arrows head to tail, because the head of the horizontal arrow is at the tail of the vertical arrow. Visualize how to do this on the figure, then click next to see it done for you.