Answer:
see below
Step-by-step explanation:
h(t) = –gt^2 + v0t + h
where g is 1/2 the gravity constant and v0 is the initial velocity and h is the initial height
h(t) = –16t^2 +49t + 0
h(t) = –16t^2 +49t
Factor out t
0 = t(-16t+49)
The zeros are at
t= 0 and -16t = -49
t = 49/16
The vertex (or max) is 1/2 way between the zeros
(0+ 49/16) /2 = 49/32 =1.53125
Round to the nearest hundredth
x = 1.53
The height is
h(1.53) = 1.53(-16 * 1.53 +49)
37.5156
To the nearest hundredth
37.52
The range is the values that height can take
0 ≤h≤37.52
There is a maximum height because eventually the effects of gravity going down outweigh the effects of the initial velocity going up
