Physics Project Conservation of momentum,energy, and projectile motion

[Wilson_Serway]

For my AP Physics Class we were given spring loaded nerf guns and asked to find a spring constant and the acceleration of the bullet before it hit the block. We had to hit a target that was on the edge of our desk and record the distance when the bullet stuck to the target. I have worked more than halfway through the problem, but have trouble when it comes to the conservation of energy and can't seem to find the acceleration.

M_b=.0136 kg
M_t=.2392 kg
X(Desk to landing place)=.3825 m
Y(Top of target to floor)=.82

To find time it takes for the bullet/target combo to reach the floor I used the y-component
X_y=X_oY+V_o(t)+1/2(a)(t)²
0=.82+1/2(-9.81)(t)²
T=-.82/-4.905=.409

To find velocity of the bullet/target combo I substituted time into the x-component
X=X_o+V_o(t)+1/2(a)(t)²
.3852= V_o(.409)
V_o=.935

To find the velocity of the bullet before it hit the target I used the conservation of momentum
M_bV_b+ M_tV_t=( M_b+ M_t)V_o
.0136Vb+.2392(0)=(.0136+.2392).935
V_b=17.38

 

[Wilson_Serway]

Ohh I forgot the spring is compressed 0.06 meters and the distance from the tip of the gun to the block is 1.77 meters.