Maximum Height of Lighter Object in Pulley System - Homework Solution

[joseg707]

Homework Statement

Two masses, 3.2kg and 2.2kg are each initially 1.80m above the ground, and the massless and frictionless pulley is 4.8m above the ground. What maximum height dies the lighter object reach after the system is released? Assume it doesn't hit the pulley.

Homework Equations

F=ma
y=y_o+v_o+1/2at²

The Attempt at a Solution

I solved for acceleration by using F=ma and got 1.8m/s².
I then solved for the velocity of the lighter object when the heavier object hit the ground by solving for the time it took for the heavier object to hit the ground and used that time to find the velocity

-1.8=-0.9t²
t=1.4

v=1.8*1.4
v=2.56

After finding the velocity I used that to find the maximum height.

y=2.56t-4.9t²
t=0, 0.522

0.522/2
t=0.261

y=3.6+2.56t-4.9t²
y=3.93333

I think I didn't take something into account or I used the wrong equation completely. Can someone help me?

 

[Redbelly98]

Looks good to me.