Answer:
90.5
Step-by-step explanation:
Velocity is a time-derivative of displacement or the height, in this case.
[tex]s(t)=-16t^2+v_0t[/tex]
[tex]v(t) = -32t+v_0[/tex]
At maximum height, the velocity is 0 and the height is 128.
Substitute these values into both equations above,
[tex]0 = -32t+v_0[/tex]
[tex]t=\dfrac{v_0}{32}[/tex]
From the first equation,
[tex]128 = -16t^2 + v_0t[/tex]
Substitute for [tex]t[/tex].
[tex]128 = -16(\dfrac{v_0}{32})^2 + v_0\times\dfrac{v_0}{32}[/tex]
[tex]128 = -v_0^2/64 + v_0^2/32[/tex]
[tex]128=\dfrac{v_0^2}{64}[/tex]
[tex]v_0^2=8192[/tex]
[tex]v_0=64\sqrt{2}=90.5[/tex]