The Problem
Say a photographer wants to capture their son playing baseball with vivid clarity, how would they know what shutter speed to set their camera at? If they find a mathematical model of the speed of the ball being thrown, the derivative of that can then be found - which can be used to find the instantaneous speed. A typical high school baseball team has pitches at around 65 miles per hour, which equates to approximately 95.333 feet per second. If this is put into the standard position function, s(t) = -16t^2 + initial velocity(t) + initial height, where s is the position, the equation ends up as: s(t) = -16t^2 + 95.333t + 5. Based on this, what would be the best shutter speed for this situation be?