Physical Push-ups

“Saffar, how many push-ups can you do in 10 seconds?” “I'll show you, $T2.”$ With that exchange, Saffar proceeded to do 15 push-ups as $T2$ (Terrence Toepker) did the timing. “I think that the upper limit is set by physical principles and not by your strength.” Assuming that you cannot pull yourself down by grabbing the floor, the shortest time down is caused by gravity acting alone. A simple physics model for this situation could be a straight, uniform plank pivoted at one end that oscillates up and down due to an elastic reflecting impulse that occurs instantaneously at the down position, shown in Fig. 1(a).