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.
You are allowed to move the arrow representing vertical velocity because you have not changed the length or direction of the vertical velocity arrow. The length represents the magnitude of the velocity, and the direction of the arrow represents the direction the velocity.
To complete the vector addition, draw a line from the tail of the horizontal velocity arrow to the tip of the vertical velocity arrow. In other words, draw the hypotenuse of a right triangle whose sides are the horizontal and vertical velocity. Visualize how you would do this. Then, go back to the graphic above and click next again to see it done for you.
The direction of the hypotenuse arrow is the direction of the take-off velocity or take-off angle. The length of the arrow is the magnitude of the take-off velocity.
The following pictures are provided for you to become more familiar with vector addition and drawing take-off velocities. By selecting each picture, you can see the vector addition performed for you.
A similiar situation occurs if you know the take-off velocity and you want to find the vertical and horizontal velocity components. Essentially you just need to draw the vertical and horizontal sides of a right triangle using the take-off velocity as the hypotenuse.
Several figures are provided below for you to practice getting the vertical and horizontal velocity from the take-off velocity.
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