Answer to Question #327600 in Mechanics | Relativity for soph

Question

Nolan Ryan reportedly had the fastest pitch in baseball, clocked at 100.9 mi/hr (45.0 m/s) If such a pitch had been directed vertically upwards at this same speed, then to what height would it have traveled (in meters)? 

Answer 1

Equations for the speed and the height of the ball are:

$v=v_0-gt.$

$h=v_0t-\frac{gt^2}{2}.$

At the highest point the speed of the ball equals to zero:

$v_0-gt=0,\newline t=\frac{v_0}{g}.$

So,

$h=\frac{v_0^2}{g}-\frac{v_0^2}{2g}=\frac{v_0^2}{2g}=\frac{45^2}{2\cdot 9.81}=103.2\space m.$