Answer
7.102 meters
Work Step by Step
At maximum height, v=0
$v(t) = \int -9.8 dt = -9.8t+v(0) = 10-9.8t $
At max height, $v(t_0)= -9.8t_0+10 =0$ or $t_0 =10/9.8 =1.02$
At this time, the height can be calculated by
$s(t)=\int (10-9.8t) dt = 10t - 4.9 t^2 + s(0) $
$s(t) = 10t - 4.9 t^2+ 2$
So, $s(t_0) = 10\times1.02 - 4.9 \times1.02^2+ 2 =\boxed{7.102}$
