Mouvement projectile

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Cegep1

Mechanics

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292 words

Reading time

2 minutes

Mouvement 2D où chaque axe effectue un MUA

[!example]- $y_{0} = 3 m, y \geq 2.24 m, x_{0} = - 8 m, x = 0 m, v_{x_{m i n}} = ?$
En $y$ :
$\begin{aligned} y (t) & = y_{0} + v_{y_{0}} t + \frac{1}{2} a_{y} t^{2} \\ 2.24 & \leq 3 + 0 t + \frac{1}{2} \cdot - 9.8 t^{2} \\ t & \leq 0.3938 \dots s \end{aligned}$
En $x$ :
$\begin{aligned} x (t) & = x_{0} + v_{x_{0}} t + \frac{1}{2} a_{x} t^{2} \\ ⟹ 0 & = x_{0} + v_{x_{m i n}} t_{m a x} + \frac{1}{2} a_{x} t_{m a x}^{2} \\ 0 & = - 8 + v_{x_{m i n}} \cdot 0.3938 \dots + \frac{1}{2} 0 \cdot 0.3938 \dots^{2} \\ v_{x_{m i n}} & \approx 20.31 \frac{m}{s} \end{aligned}$

[!example]- $y_{0} = 3 m, y = 0 m, x_{0} = - 8 m, x \leq 9 m, v_{x_{m a x}} = ?$
En $y$ :
$\begin{aligned} y (t) & = y_{0} + v_{y_{0}} t + \frac{1}{2} a_{y} t^{2} \\ 0 & = 3 + 0 t + \frac{1}{2} \cdot - 9.8 t^{2} \\ t & = 0.7824 \dots s \end{aligned}$
En $x$ :
$\begin{aligned} x (t) & = x_{0} + v_{x_{0}} t + \frac{1}{2} a_{x} t^{2} \\ ⟹ 9 & = x_{0} + v_{x_{m a x}} t + \frac{1}{2} a_{x} t^{2} \\ 9 & = - 8 + v_{x_{m a x}} \cdot 0.7824 \dots + \frac{1}{2} \cdot 0 t^{2} \\ v_{x_{m a x}} & \approx 21.73 \frac{m}{s} \end{aligned}$

[!example]- $θ = 30^{\circ}, x_{0} = 0 m, x = 63 m, y_{0} = 2 m, y = 0, v_{x_{0}} = ?$
En $x$ :
$\begin{aligned} x (t) & = x_{0} + v_{x_{0}} t + \frac{1}{2} a_{x} t^{2} \\ 63 & = 0 + \cos 30^{\circ} v_{0} t + \frac{1}{2} \cdot 0 t^{2} \\ t & = \frac{63}{\cos 30^{\circ} v_{0}} \end{aligned}$
En $y$ :
$\begin{aligned} y (t) & = y_{0} + v_{y_{0}} t + \frac{1}{2} a_{y} t^{2} \\ 0 & = 2 + \sin 30^{\circ} v_{0} t + \frac{1}{2} \cdot - 9.8 t^{2} \\ ⟹ 0 & = - 4.6 {(\frac{63}{\cos 30^{\circ} v_{0}})}^{2} + \sin 30^{\circ} v_{0} (\frac{63}{\cos 30^{\circ} v_{0}}) + 2 \\ 0 & = - \frac{24343.2}{v_{0}^{2}} + 21 \sqrt{3} + 2 \\ v_{0} & = 25.1869 \dots \frac{m}{s} \end{aligned}$ $v_{x_{0}} = \cos 30^{\circ} v_{0} = 25.1869 \dots \frac{m}{s}$
$x_{0} = 0 m, x = 0.7 m, v_{x_{0}} = 0 \frac{m}{s}, v_{x} = 25.1869 \dots \frac{m}{s^{2}}, a_{x} = ?$
$\begin{aligned} v_{x} (x)^{2} & = v_{x_{0}}^{2} + 2 a_{x} (x - x_{0}) \\ 25.1869 \dots^{2} & = 0^{2} + 2 a_{x} (0.7 - 0) \\ a_{x} & \approx 453.1 \frac{m}{s^{2}} \end{aligned}$

Contributors

Ajitani Hifumi

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Last edited about 2 months ago

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Mouvement projectile ​

Contributors

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Mouvement projectile