Answer
The block will rise up to a height of 0.831 meters.
Work Step by Step
Let $m$ be the mass of a bullet and let $M$ be the mass of the block. Let $v$ be the initial speed of the bullet.
We can use conservation of momentum to find the speed $v'$ just after the collision:
$m~v = (m+M)~v'$
We can use conservation of energy to find the relationship between $v'$ and the height $h$ reached by the block:
$\frac{1}{2}(m+M)~(v')^2 = (m+M)~gh$
$v' = \sqrt{2gh}$
We can replace $v'$ in the first equation above.
$m~v = (m+M)\sqrt{2gh}$
$h = (\frac{m}{m+M})^2~\frac{v^2}{2g}$
$h = (\frac{0.0250~kg}{0.0250~kg+1.40~kg})^2~\frac{(230~m/s)^2}{(2)(9.80~m/s^2)}$
$h = 0.831~m$
The block will rise up to a height of 0.831 meters.