平抛运动性质¶
基础¶
\(\Delta v = gt\)
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:
\(\left\{ \begin{aligned} v &= \sqrt{v_x^2 + v_y^2} \\ x &= \sqrt{x^2 + y^2} \\ \end{aligned} \right.\)
推论¶
\(\because \left\{ \begin{aligned} \tan{\theta} &= \dfrac{v_y}{v_x} = \dfrac{2y_A}{x_A} \\ \tan{\alpha} &= \dfrac{y_A}{x_A} \end{aligned} \right.\)
\(\therefore \tan{\theta} = 2 \tan{\alpha}\)
\(\tan{\theta} = 2 \tan{\alpha}\)
\(x_b = \frac{1}{2} x_a\)