Jangkauan Maksimum Gerak Parabola pada Bidang Miring

[Albert Erros]

Gloria in excelsis Deo.

$$a_x = -g\sin\alpha$$
$$a_y = -g\cos\alpha$$
$$v_x = v_0\cos\beta - gt\sin\alpha$$
$$v_y = v_0\sin\beta - gt\cos\alpha$$
$$x = v_0t\cos\beta - (1/2)gt^2\sin\alpha$$
$$y = v_0t\sin\beta - (1/2)gt^2\cos\alpha$$
$$y = 0$$
$$t = T = (2v_0\sin\beta)/(g\cos\alpha)$$
$$R = v_0T\cos\beta - (1/2)gT^2\sin\alpha$$
$$R = \frac{2v_0^2\sin\beta}{g\cos\alpha}(\cos\beta - \sin\beta\tan\alpha)$$
$$dR/d\beta = 0$$
$$\tan2\beta = \cot\alpha$$
$$\beta = \pi/4 - \alpha/2$$

Berkah Dalem Gusti.