Tracy became interested in the maximal height for throwing a ball. On the internet, she finds that the maximum pitching speed of professional baseball players is 150 feet per second (about 105 miles per hour).
The equation for the height y (in feet) after t seconds of a ball thrown vertically in the air at that speed is y=-16t^2+ 150t
At what time would the ball reach a height of 400 feet?
400 = -16 t^2 + 150 t
16 t^2 -150 t = -400
roots are complex, the ball never gets that high
kinetic energy at ground = (1/2)mv^2
= 75*150 m = 11,250 m
potential energy at top = m g h =32 m h
so h = 11250/32 = 352 feet max height