# Kinematics

Kinematics are governed by the equations:

* Pro Tip: If you have n unknown variables, then you need n equations to find those unknowns (e.g. two unknowns means you’ll use two equations to find the unknowns) *

### Method for Solving Kinematic Equations

Draw a picture!

Write down every variable you

*know*, and every variable you*don’t know / want to find*. Sometimes known variables are super obvious (e.g. if a ball is launched horizontally, then you know that its starting y-velocity, v_y0 = 0)Go through your kinematic equations and find an equation where you know every variable except one, and then solve for that variable.

Repeat step 3 until you know all of your unknowns!

* Note: There are many different ways to solve just 1 kinematics problem so don’t be afraid to mess around and try different ways until something works!

### Typical Example

You fire a potato from a cannon in an attempt to hit your drunk uncle’s foot 40 meters away. You fire the potato at an initial speed of 20 m/s at an angle of 30° above the ground. Will the potato reach your uncle’s foot?

1) Draw a picture

2) Write down knowns and unknowns:

3) So we need two equations to find x*t and t. Looking through our kinematics equations, we can’t find an equation where we know everything except x_t, but we can find one where we know everything but t! Look at the first half of the potato’s journey. *When it reaches its maximum height, *v_*yt = 0, so use:

*But this is only half of the potato’s flight*. Since it takes just as much time for the potato to reach its max height as it does for the potato to come back down, the total flight time is:

4) Now we know everything but x_t, which we can find with this equation:

*So the potato does not reach your drunk uncle’s foot*

* Bonus question: If you keep your launch angle the same, what velocity would you need to shoot the potato out of the cannon at in order for it to hit your uncle’s foot?