Given that the height of the ball has been modeled by h=120t-16t^2, the reasonable range will be found as follows:
maximum height is attained when h'(t)=0
given h=120t-16t^2
h'(t)=120-32t=0
thus solving for t, we get:
t=3.75 sec
thus the maximum time attained will be:
120(3.75)-16(3.75)^2=225 ft
Therefore the reasonable range will be [0≤h(t)≤225]
