The Euro 2020 tournament has been a highlight of our summer so far, especially since we’ve got a serious soccer player in the family. We live in Berlin so we were rooting for Germany until they got knocked out by England in the round of 16.

There are so many physics lessons to be learned from soccer, so why not turn some of that watching and playing time into a short lesson?

In high school physics there are many opportunities to use soccer to spark students’ interest in studying the laws of energy and motion. Projectile motion, conservation of energy, Newtons laws of motion, and the Magnus effect are just a few of the concepts that players unknowingly use while plying their craft.

In today’s post we examine how to solve two different problems when the launch angle and distance are given:

(1) What initial velocity is needed to hit the center circle from the top of the goalie’s box?

(2) What initial velocity is needed to hit the crossbar from the edge of the center circle? See diagram below.

In both cases there are two unknowns, the time in the air *t* and the initial velocity *v _{i}. *Therefore we will need two equations to solve these problems.

The first equation comes from deconstructing the initial velocity vector into its *x* and *y* components as shown below:

v_{ix} = cos Θ • v_{i}

v_{iy} = sin Θ • v_{i}

Because there is no acceleration in the *x* direction, we can use the standard velocity equation to come up with an equation for the time in terms of the initial velocity.

v_{ix} = x/t

t = x/v_{ix}

Substituting the equation for the x component of the initial velocity yields an equation for the time in terms of the initial velocity:

t = x/cos Θ • v_{i}

The second equation is one of my favorite kinematic equations:

Δy = vi • t + ½ • a • t^{2}

Substituting equation 1 into equation 2 we will have a single equation with one variable, our unknown: v_{i}.

Still unclear about these concepts? Check out our YouTube video to see if Sam can hit the crossbar and for a complete step-by-step explanation for determining the initial velocity needed to do so.

And don’t miss the penalty shootout between the father and son to see who wins bragging rights.