Movement

Parabola

Curved motion with constant acceleration

Note: Sometimes the speed cannot decease to 0.

Procedure: Newton's second law of The whole system

$F_x = m_1 a_1x + m_2 + a_2x + ...$

Exercise

1

Solution

Procedure 2

$\left\lvert \frac{F_x}{F_y} \right\rvert = \left\lvert \frac{\Delta v_x}{\Delta v_y} \right\rvert$ (deduced from impulse-momentum theorem)

Horizontal cast movement

$y = \frac{1}{2} a t^2 = \frac{1}{2} a (\frac{x}{v_0})^2 = \frac{F}{2m v_0^2} x^2 = \frac{F}{4E_{k0}} x^2$

$tan \theta = y' = \frac{F}{m v_0^2} x = \frac{F}{2E_{k0}} x$

$tan \theta_v = 2 tan \theta$