Question 1178898
the vertex t value is at -b/2a or -29.4/-9.8 or 3 seconds
the maximum height is at h(3)=-44.1+88.2+1=45.1 m
solve for h=40
so -4.9t^2+29.4t+1=40
and -4.9t^2+29.4t-39=0
or 4.9t^2-29.4t+39=0
t=(1/9.8)(29.4+/-sqrt (99.96); sqrt term=10.0
t=1.98 sec and t=4.02 sec
it is above 40 m for 2.04 sec
it hits 0 at -4.9t^2+29..4t-1=0=4.9t^2-29.4t+1
the positive root is t=(1/9.8)*(29.4+sqrt883.86); sqrt term=29.73
t=6.03 sec

{{{graph(300,300,-10,10,-10,50,40,-4.9x^2+29.4x+1)}}}