View source for Eksperimentti: hyppykorkeuden määrittäminen lentoajalla.

== Introduction ==

[[File:ForcePlate jumping1.svg|thumb|Force exerted on the force plate]]

Jumping on the force plate you can feel the force. We use time of flight method to estimate the height of the jump.

== Theory ==

[[File:ForcePlate jumping2 timeOfFlight.svg|thumb]]

<math>s = s_0 + v_0 t + \tfrac12 at^2</math> and thus we have <math>h = v_0 t - \tfrac12 gt^2</math> because <math>h_0=0</math> and <math>a=-g = -9.81m/s^2</math>. However, for the velocity we have <math>v = v_0 - gt</math> and at the maximum height we have that <math>v=0</math>, and thus <math>v_0 = gt_m</math>. Combining these two we have

<math>
\begin{matrix}
h &= v_0 t - \tfrac12 gt^2 \\
  &= gt_m^2 - \tfrac12 gt_m^2 \\
  &= \tfrac12 gt_m^2
\end{matrix}
</math>

The time at the maximum height (<math>t_m</math>) will be half of the flight time.

== Example == 

In the experiment, we have <math>t_m = 0.16</math> s, which gives <math> h = \tfrac12 gt_m^2 = \frac12 \times 9.81 \times 0.16^2 = 0.13</math> m. 

The takeoff velocity is <math>v_0 = gt_m = 9.81 m/s^2 \times 0.16 s =  1.5696 m/s</math>.