Problems dealing with motion are usually the first that students of physics will encounter. Concepts like time, velocity and acceleration are interrelated by formulas that students can rearrange with the help of algebra to apply to different circumstances.

Students can calculate the height of a jump, for instance, from more than one starting point. The height of the jump can be calculated if the acceleration and either the initial velocity or the total time in the air is known.

Write an expression for time in terms of change in velocity, using the formula

where *v*_{f} is final velocity, *g* is the acceleration due to gravity, *t* is time, and *v*_{i} is initial velocity.

## Time of Flight

Solve the equation for *t*

Therefore, the amount of time is equal to the change in velocity divided by the acceleration due to gravity.

## Calculate Time to Reach Highest Point

Calculate the amount of time to reach the highest point of the jump. At the highest point, velocity (*v*_{f}) is zero. Use 9.8 m/s² for the acceleration due to gravity. For example, if the initial velocity is 1.37 m/s, time to reach maximum height is:

## Calculate Initial Velocity from Total Time of Flight

The initial velocity *v*_{i} can be calculated using the time to reach the jump height

For example, if the total time is 0.14 seconds:

## Vertical Jump Physics Equation

Calculate the jump height using the formula

where *s*_{f} is the final position and *s*_{i} is the initial position. Since jump height is the difference between the final and initial position

simplify the formula to

and calculate:

#### Tips

Create your own jump height calculator by programming the jump height formula into your graphing calculator!

References

Resources

Tips

- Derive the formula vi = -g*T/2 from the formula sf = si + vi*T + (g*T²)/2. The initial and final positions are the same before and after the jump, so set them to zero and factor: T(vi + g*T/2) = 0. Setting the factors equal to zero gives you two results: T = 0 and vi + g*T/2 = 0. The first indicates that no time is required for your initial position to equal your final, and the second result represents the amount of time for a body to rise and fall back down to where it was. Solve the second expression for initial velocity.

About the Author

Mike Gamble started writing professionally in 2011 for Demand Media Studios. Having worked as a line mechanic, landscaper, custodian, carpenter, web developer and disk jockey, he hopes to bring fresh insight into the topics he writes about from a variety of experiences.

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