When you think about solving problems with things flying through the air, there are a few simple formulas that can help a lot! Here are the main ones to remember:

1. Vertical Motion:

   • To find out how high something is at any time $t$, you can use this formula: $h(t) = h_0 + v_{0y}t - \frac{1}{2}gt^2$ Here,
   • $h_0$ is where you start (the initial height),
   • $v_{0y}$ is how fast it moves up or down at the start (initial vertical velocity),
   • $g$ is how fast things fall due to gravity (about $9.81 \, m/s^2$).

2. Horizontal Motion:

   • For figuring out how far something goes side to side, use this: $x(t) = v_{0x}t$ Here,
   • $v_{0x}$ is how fast it moves sideways at the start (initial horizontal velocity).

3. Time of Flight:

   • If you want to know how long something stays in the air before it lands at the same height again, you can find it with: $T = \frac{2v_{0y}}{g}$

By using these simple formulas, you can tackle any problem about things moving through the air with confidence!