To calculate the vertical displacement all you need is the vertical take-off velocity. There are several ways to do this. The easiest is to first calculate the time it took to get from take-off to the top of the jump. This is commonly referred to as time-up
Time-up can be calculated form the equation that:
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The equation:
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When calculating time-up, the final velocity is the vertical velocity at the top of the jump, the initial velocity is the vertical take-off velocity and acceleration is the acceleration due to gravity.
Re-arrange the equation to calculate time-up:
You know the vertical take-off velocity, or you can calculate it using SOHCATOA, and you also know that at the top of the jump the vertical velocity of the skater is zero, as was discussed previously.
Try calculating Time-up in the following example. To see the solution, just click on the solution button.
If your answer doesn't agree, go to the help page for tips on working through these types of problems.
Once you have calculated time-up, you can get the vertical displacement from another equation.
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The equation:
 can be used to calculate displacement for any object undergoing constant acceleration. |
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The displacement you want to calculate is the vertical displacement, or height of the jump. This means you must use velocity and time values which correspond to this particular displacement. For example, you need to use the vertical take-off velocity for initial velocity since you are going to calculate vertical displacement. You also need to use time-up for the time, since you are calculating the vertical displacement up, the height.
The take-off velocity and angle for a jump are provided in the following illustration. Try calculating jump height and time-up.
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