抛物线运动

平抛运动性质¶

$\Delta v = gt$

水平:

$ \left{ \begin{aligned} v_x &= v_0 \ x &= v_0 t \end{aligned} \right. $

竖直:

$ \left{ \begin{aligned} v_y &= gt \ y &= \frac{1}{2} g t^2 \ \end{aligned} \right. $

合成:

$ \left{ \begin{aligned} v &= \sqrt{v_x^2 + v_y^2} \ x &= \sqrt{x^2 + y^2} \ \end{aligned} \right. $

$ \because \left{ \begin{aligned} \tan{\theta} &= \dfrac{v_y}{v_x} = \dfrac{2y_A}{x_A} \ \tan{\alpha} &= \dfrac{y_A}{x_A} \end{aligned} \right. $

$ \therefore \tan{\theta} = 2 \tan{\alpha}

$\tan{\theta} = 2 \tan{\alpha}$

$x_b = \frac{1}{2} x_a$