The Physics of a Viral Video

For those that remember and were fans of Vine, there was a viral video in 2014 of an 11 year old boy screaming with happy enthusiasm while being hit in the head with a basketball. I wondered, how does this kid not have any brain damage or a concussion from getting hit so hard? Well, I was able to find the answer with physics!

The basketball bouncing off the kid’s head was an elastic collision: thus, energy and momentum had to be conserved. First, I analyzed the momentum of the system:

Δpsys= 0kgms → p’ = p

mcvc’+mbvb’=mcvc+mbvb

In the video, the boy does not have an initial velocity, and the basketball only comes in contact with his head. According to GW Osteopathy (https://www.gwosteopathy.co.uk/much-head-weigh/), the average human head has a mass of about 5kg. Because this is a child, I used 4.5 kg as the mass of his head. A standard NBA basketball (as in the video) has a mass of 0.62 kg. To find the initial velocity of the basketball, I used Tracker software that is used in the lab. Thus, the initial velocity of the basketball was found to be -5.52 m/s. I was able to substitute these values into the equation above:

mcvc’+mbvb’=mcvc+mbvb

(4.5 kg)vc’+(0.62 kg)vb’=(36 kg)(0 m/s)+(0.62 kg)(-5.52 m/s)

Because this was an elastic collision, energy was also conserved. Thus, the following equation could also be used:

vc+vc’=vb+vb’

0+vc’=(-5.52 m/s)+vb’

vc’=(-5.52 m/s)+vb’

This was then substituted into the equation for conservation of momentum, and both final velocities were calculated:

(4.5 kg)(-5.52 m/s+vb’)+(0.62 kg)vb’=(36 kg)(0 m/s)+(0.62 kg)(-5.52 m/s)

vb’= 4.18 m/s

vc’=(-5.52 m/s)+vb’

vc’=-5.52 m/s+4.18 m/s

vc’=-1.34 m/s

With the initial and final velocities of both the child and the basketball, the force on the child’s head could be calculated using impulse. Tracker software also showed that the collision occurred over 0.05 seconds:

ΣFΔt=Δp

F(0.05 s)=(4.5 kg)(-1.34 m/s - 0 m/s)

F=-120.6 N

It is known that the human head can withstand about 90 g’s before sustaining a concussion. Thus, this force was converted into an acceleration in g’s:

F=ma

-120.6 N=(4.5 kg) a

a=26.8 m/s2=2.73 g

The 2.73 g’s that the boy experiences in this video is much less than the 90 g’s needed to get a concussion! If you’re curious about the viral video, it can be found in this Buzzfeed article.