Fysik opgaver Fodbold (Rep)


Opgave 7.1

A
LaTex: \begin{eqnarray} \alpha &=& 20^\circ\\ v_0 &=& 16 \frac{m}{s}\\ t_{maks} &=& \frac{2\cdot v_0 \cdot sin( \alpha )}{g}\\ t_{top} &=& \frac{t_{maks}}{2} = 0,557s\\ \end{eqnarray}
B
LaTex: \begin{eqnarray} x_{top}&=&\frac{\frac{v_0^2 \cdot sin( 2\cdot \alpha )}{g}}{2} = 8,38 m\\ y_{top}&=&\frac{v_0^2 \cdot sin( \alpha )^2 }{2\cdot g} = 1,52 m\\ \end{eqnarray}
C
LaTex: \begin{eqnarray} x_{maks} &=& x_{top}\cdot 2 = 16,86m\\ t_{maks} &=& t_{top}\cdot 2 = 1,114 s\\ \end{eqnarray}
D
LaTex: \begin{eqnarray} t &=& 0,7 s\\ V_x &=& V_0\cdot \cos(\alpha)\\ x &=& V_x\cdot t = 10,52m\\ y &=& \frac{1}{2}\cdot -G\cdot t^2 + V_0\cdot\sin(\alpha)\cdot t = 1,42m\\ \end{eqnarray}

Opgave 7.2

A
LaTex: \begin{eqnarray} h &=& 400m\\ v_x &=& 350 \frac{km}{h} = 97,22 \frac{m}{s}\\ \end{eqnarray}
Udkast ved 0 ; 400.
B
LaTex: \begin{eqnarray} t &=& \sqrt{\frac{2\cdot h}{g}} = 9,03 s\\ \end{eqnarray}
C
LaTex: \begin{eqnarray} s &=& v_x\cdot t = 877,52 m\\ \end{eqnarray}
D
LaTex: \begin{eqnarray} v_y &=& g\cdot t\\ \vec{v} &=& {v_x \choose v_y}\\ \angle &=& \tan^{-1}{\frac{v_y}{v_x}} = 42,35^\circ\\ v &=& \sqrt{v_x^2+v_y^2} = 131,59\frac{m}{s}\\ \end{eqnarray}

Opgave 7.3

Bevægelsens tid
LaTex: \begin{eqnarray} s &=& 175 m\\ \alpha &=& 17^\circ\\ x &=& s\\ y &=& 0\\ y &=& -\frac{g \cdot x^{2} }{2v^{2}_{0} \cdot cos( \alpha )^{2} }+tan( \alpha ) \cdot x\\ &\downarrow &\\ v_0 &=& \sqrt{ \frac{ -g\cdot x^2}{(y-tan( \alpha ) \cdot x) \cdot 2 \cdot cos( \alpha )^2}} = 55,44 \frac{m}{s}\\ t_{maks} &=& \frac{2\cdot v_0 \cdot sin( \alpha )}{g} = 3,3 s\\ \end{eqnarray}
Starthastighed
LaTex: \begin{eqnarray} v_0 &=& 55,44\frac{m}{s}\\ \end{eqnarray}
Maks højde
LaTex: \begin{eqnarray} y_{top} &=& \frac{v_0^2 \cdot sin( \alpha )^2 }{2\cdot g} = 13,38m\\ \end{eqnarray}
Hentet fra "http://jopsen.dk/wiki/Fysik_opgaver_Fodbold_%28Rep%29/"