Patrick Mahomes is trying to break the longest touchdown record. He wants to use the very best ball to compete. Mahomes experiment in practice using a leather ball, rubber ball, and foam football to see which one will go the farthest

Engines for propeller-driven aircraft are limited in their maximum rotational speed by the fact that the tip speed of the propeller must not approach the speed of sound in air (mach i). taking 6 ft as a typical diameter for a propeller of a light airplane and 1100 fils as the speed of sound, find the upper limit on the rpm (revolutions per minute) of the propeller shaft.