Answer
The chunks of ice will go up to a height of 1.84 meters.
Work Step by Step
We can use conservation of momentum to find the speed after the collision.
$m_2v_2 = m_1v_1$
$v_2 = \frac{m_1v_1}{m_2}$
$v_2 = \frac{(5.00~kg)(12.0~m/s)}{10.00~kg}$
$v_2 = 6.00~m/s$
When the blocks reach maximum height, the potential energy will be equal to the kinetic energy at the bottom of the hill.
$PE = K$
$m_2~gh = \frac{1}{2}m_2~v_2^2$
$h = \frac{v_2^2}{2g}$
$h = \frac{(6.00~m/s)^2}{(2)(9.80~m/s^2)}$
$h = 1.84~m$
The chunks of ice will go up to a height of 1.84 meters.
