A human skull can withstand 100 kPa before fracturing. A baseball, with an impact area 0.003 m^{2} and a weight of 0.15 kg, is launched from a pitching machine, a distance of 20 meters, towards a skull. How long would it take for the baseball to travel if the skull was cracked?

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Correct Answer: **A.** *sqrt(1/50) s*

We would like to know how long. So to find a time we will need to know a distance and a rate. We are given a distance, but we will need to find both the acceleration and the velocity required to break a skull. We can assume the baseball started at rest before it was launched so its initial velocity is zero. To find the acceleration we can use Newton’s 2nd Law.

Now that we have the acceleration, we can use the kinematic equations to solve for time. Remember there is no initial velocity.

A professional pitcher can throw a baseball up to 105 mph. In our problem, we can calculate an average speed of around 140 m/s that is about 315 mph! It is also interesting to note that it takes about 1 atm (101 kPa) until a skull breaks. Hats off to those who play baseball.

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Photo attributed to ScientificRelevance.