maximum height

(I'm not very good at functions... but I think this is correct)

h(t)=44t-16t^2

t=44/32=11/8

h(t)=44(11/8)-16(11/8)^2=121/2-121/4=$\boxed{\frac{121}4}$

-16t^2 + 44t      = h       max h will occur at t = - b/2a =  -  44/(2*-16) =  1.375 sec  

     Use this value of t to calc height

 

-16 ( 1.375)^2 + 44 ( 1.375) = 30.25 ft max