# What is the projectile motion equation?

Apr 28, 2015

Basically, any of the kinematic equations works, if you know when to use which equation.

For a projectile shot at an angle, to find time, first consider the first half of the motion. You can set up a table to organize what you have and what you need to figure out which kinematic equation to use.
For example: A child kicks a ball with initial velocity of $15 \frac{m}{s}$ at an angle of ${30}^{o}$ with the horizontal. How long is the ball in the air?

You can start with the table of givens. For time you're going to need the y-component of the velocity.
${v}_{i} \rightarrow 15 \cdot \sin \left(30\right) = 7.5 \frac{m}{s}$
${v}_{f} \rightarrow 0 \frac{m}{s}$
$a \rightarrow - 9.8 \frac{m}{s} ^ 2$
$t \rightarrow F I N D$
$\Delta x \rightarrow u n k n o w n$

You can use the kinematic equation ${v}_{f} = {v}_{i} + a t$. Substitute:
$0 = 7.5 + \left(- 9.8\right) t$
$t = 0.77 s$
REMEMBER that this is only for the first half of the motion, so multiply the calculated time by $2$ to find the total time. In this case $2 \cdot 0.77 = 1.54 s$

So, the moral is, if you can identify what the question is asking for, and you can find the givens, organize them into a table similar to the one I made, and chose the appropriate kinematic equation, you should be fine. Sorry if this was a bit long.