Eksperimentti: hyppykorkeuden määrittäminen lentoajalla.

Introduction

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

$s=s_{0}+v_{0}t+{\tfrac {1}{2}}at^{2}$ and thus we have $h=v_{0}t-{\tfrac {1}{2}}gt^{2}$ because $h_{0}=0$ and $a=-g=-9.81m/s^{2}$. However, for the velocity we have $v=v_{0}-gt$ and at the maximum height we have that $v=0$, and thus $v_{0}=gt_{m}$. Combining these two we have

${\begin{matrix}h&=v_{0}t-{\tfrac {1}{2}}gt^{2}\\&=gt_{m}^{2}-{\tfrac {1}{2}}gt_{m}^{2}\\&={\tfrac {1}{2}}gt_{m}^{2}\end{matrix}}$

The time at the maximum height ($t_{m}$) will be half of the flight time.

Example

In the experiment, we have $t_{m}=0.16$ s, which gives $h={\tfrac {1}{2}}gt_{m}^{2}={\frac {1}{2}}\times 9.81\times 0.16^{2}=0.13$ m.

The takeoff velocity is $v_{0}=gt_{m}=9.81m/s^{2}\times 0.16s=1.5696m/s$.