a)
$\frac{1}{2} v_{z}^{2}=g H \Rightarrow v_{z}=\sqrt{2 g H}$
Speed at ground is given as:
$\sqrt{v_{s}^{2}+v_{z}^{2}}=\sqrt{v_{s}^{2}+2 g H}$
b)$\frac{1}{2} m v_{s}^{2}+m g H$ is the total energy of the ball when it hits the ground.
Hence, a) and b) both have the same speed.