LEC6

• Projectile Motion.

Projectile Motion

• When the path of a particle is determined solely by gravity and air resistance (ignored for us) it is called projectile motion.

$$g=9.8m{s}^{-2}$$

• Since $x$ and $y$ components behave independently, gravity affects only the $y$-component.

$$a_x=0;a_y=-g$$

(depends on our choice of coordinates)

For x:

$$\begin{array}{r}{a}_x=0\\ v_x=v_{0x}\\ x=x_0+v_{0x}t\end{array}$$

For y:

$$\begin{array}{r}{a}_y=-g\\ v_y=v_{0y}-gt\\ y=y_0+v_{0y}t-\frac{1}{2}g{t}^2\end{array}$$

Splitting into Components

$$\begin{array}{r}{v}_{0y}=v_0\sin \theta \\ v_{0x}=v_0\cos \theta \\ \\ x=x_0+v_{0x}t\\ ⟹v_{0x}=\frac{x}{t}\\ v_0\cos \theta =\frac{x}{t}\\ t=\frac{x}{v_0\cos \theta }\\ ⟹y=v_{0y}t-\frac{1}{2}g{t}^3\\ =v_o\sin \theta \cdot \frac{x}{v_0\cos \theta }-\frac{g{x}^2}{2v_0\cos \theta }\\ y=x\tan \theta -\frac{g{x}^2}{2v_0\cos \theta }\end{array}$$

If car is de-accelerating, net acceleration points behind center.