Chapter summary

Projectiles are objects that move through the air.
Objects that move up and down (vertical projectiles) on the earth accelerate with a constant acceleration g which is approximately equal to 9,8 m·s⁻² directed downwards towards the centre of the earth.
The equations of motion can be used to solve vertical projectile problems.

$\begin{matrix} v_{f} & = & v_{i} + g t \\ Δ x & = & \frac{(v_{i} + v_{f})}{2} t \\ Δ x & = & v_{i} t + \frac{1}{2} g t^{2} \\ v_{f}^{2} & = & v_{i}^{2} + 2 g Δ x \end{matrix}$ (1)
Graphs for vertical projectile motion are similar to graphs for motion at constant acceleration. If upwards is taken as positive the $Δ x$ vs t, v vs t ans a vs t graphs for an object being thrown upwards look like this:
Momentum is conserved in one and two dimensions.

$\begin{matrix} p & = & m v \\ Δ p & = & m Δ v \\ Δ p & = & F Δ t \end{matrix}$ (2)
An elastic collision is a collision where both momentum and kinetic energy is conserved.

$\begin{matrix} p_{before} & = & p_{after} \\ K E_{before} & = & K E_{after} \end{matrix}$ (3)
An inelastic collision is where momentum is conserved but kinetic energy is not conserved.

$\begin{matrix} p_{before} & = & p_{after} \\ K E_{before} & \neq & K E_{after} \end{matrix}$ (4)
The frame of reference is the point of view from which a system is observed.

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