Assuming no friction and that dropping the brick does not add any force towards the cart's motion:
We considered momentum to be conserved, so before the brick is dropped, the cart's momentum is mass * velocity, or 2.6 kg * 28.2 cm/s = 73.32 kg-cm/s.
If the brick has mass x, then the new momentum would be (2.6 + x) kg * 15.7 cm/s. We equate this to 73.32.
73.32 = (2.6 + x)*15.7
x = 2.07
Therefore the brick has a mass of 2.07 kg
