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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_m = 0.16} s, which gives Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h = \tfrac12 gt_m^2 = \frac12 \times 9.81 \times 0.16^2 = 0.13} m.

The takeoff velocity is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_0 = gt_m = 9.81 m/s^2 \times 0.16 s = 1.5696 m/s} .