Rifle Ball Through a Three-Inch Plank

A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.  Its velocity on entering the plank is 1000 feet/second, and on leaving the plank is 500 feet/second.  How long does it take the ball to traverse the plank? 

Problems in Differential Calculus, Byerly, 1895

Click here to reveal the answer