Write an expression for time in terms of change in velocity, using the formula vf = g*t + vi, where vf is final velocity, g is the acceleration due to gravity, t is time, and vi is initial velocity. Solve the equation for t: t = (vf - vi)/g. Therefore, the amount of time is equal to the change in velocity divided by the acceleration due to gravity.
Calculate the amount of time to reach the highest point of the jump. At the highest point, velocity is zero, so with the initial velocity and the formula t = (vf - vi)/g, you can find time. Use -9.8 meters/second² for the acceleration due to gravity. For example, if the initial velocity is 1.37 meters/second, time is:
t = (0 - 1.37)/(-9.8)
t = 0.14 seconds
If you know the total time in the air, you can calculate the initial velocity with the formula vi = -g*T/2, where T is total time. Total time is also twice the time to reach the highest point, so t = T/2. For example, if the total time is 0.28 seconds:
vi = -(-9.8 * 0.28)/2
vi = 1.37 meters per second
t = 0.28/2
t = 0.14 seconds
Calculate the jump height using the formula sf = si + vi*t + (g*t²)/2, where sf is the final position and si is the initial position. Since jump height is the difference between the final and initial position, h = (sf - si), simplify the formula to h = vi*t + (g*t²)/2, and calculate:
h = (1.37*0.14) + (-9.8*0.14²)/2
h = 0.19 - 0.10
h = 0.09 meters