Answer
Height: $5.5~m$
Initial speed: $11~m/s$
Work Step by Step
We know that
$T=0.75s+\frac{0.75s}{2}$
$\implies T=1.125s$
The initial speed is given as
$v_{f1}=v_{1i}-gT$
This can be rearranged as:
as $v_{f1}=0m/s$
$\implies v_{i1}=gT$
We plug in the known values to obtain:
$v_{i1}=(9.8m/s^2)(1.125s)$
$v_{i1}=11m/s$
Similarly $v_p=11m/s-(9.8m/s^2(0.75s))$
$v_p=3.7m/s$
Now $h=(\frac{v_{i1}+v_p}{2})t_1$
We plug in the known values to obtain:
$h=(\frac{11+3.7}{2})(0.75s)$
$h=5.5m$
