Question

The two masses in the Atwood's machine shown in the figure are initially at rest at the same height. After they are released, the large mass, , falls through a height and hits the floor, and the small mass, , rises through a height . Find the speed of the masses just before lands, giving your answer in terms of , , , and . Assume the ropes and pulley have negligible mass and that friction can be ignored. Evaluate your answer to part A for the case = 1.7 , = 3.9 , and = 5.1 .

Answer 1

I advise a conservation of energy approach to get the total kinetic energy when the heavier mass hits the floor. The ratio of kinetic energies of the masses remains equals to the mass ratio, since they both have the same speed at all times.

You have missing symbols in your statements such as
<<..for the case = 1.7 , = 3.9 , and = 5.1 >>
therefore I cannot be of further assistance without additional information.