Kinematics are governed by the equations:

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* 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

  1. Draw a picture!

  2. 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)

  3. Go through your kinematic equations and find an equation where you know every variable except one, and then solve for that variable.

  4. 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 xt 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?