Answer
$\Delta x_s=1.5m$ (smaller block)
$\Delta x_b=0.38m$ (bigger block)
Work Step by Step
1. Calculate final velocity of block of mass M given that all initial PE gets converted to KE
$PE=Mg(0.35m)=3.5M$
$v_i=\sqrt{\frac{7M}{M}}=2.65m/s$
2. Calculate horizontal velocities of 2 blocks after collision
$M(2.65m/s)=M(v_b)+0.5M(v_s)$
$\frac{M(2.65m/s)^2}{2}=\frac{M(v_b)^2}{2}+\frac{0.5M(v_s)^2}{2}$
$v_s=3.53m/s$
$v_b=0.883m/s$
3. Calculate time it takes for blocks to reach ground.
$-0.95m=\frac{(-10m/s^2)t^2}{2}$
$t=0.436s$
4. Calculate $\Delta x$ for each block
$\Delta x_s=(3.53m/s)(0.436s)=1.5m$
$\Delta x_b=(0.883m/s)(0.436s)=0.38m$