Answer:
ok so here we go
Step-by-step explanation:
(ma)(va,1)+(mb)(vb,1)=(ma+mb)(v2)(ma)(va,1)+(mb)(vb,1)=(ma+mb)(v2).
Plugging in the givens results in (.008)(va,1)=v2(.008)(va,1)=v2.
Then, I considered the energies of the system as a whole. Spring force is conservative.
I reason that at the point at which the spring is at maximum compression of .15 m, the final velocity of the block is zero.
So, (1/2)(ma)(va,1)2=(1/2)(300)(.15)2(1/2)(ma)(va,1)2=(1/2)(300)(.15)2
I get 300 as the spring constant because F=kxF=kx.
Solving for va,1va,1, I got 29.0 m/s. I then multiplied 29.0 by .008 to get the velocity of the system, v2
(1/2)(ma+mb)(v2)2