Bullet fired into block attached to spring

[tsdemers]

A 11-g bullet traveling at 208 m/s is fired into a 0.422 kg wooden block anchored to a 100N/m spring. If the speed of the bullet is not known but it is observed that the spring is compressed 53.1 cm, what was the speed of the bullet to the nearest m/s?

Can someone help me out on where to get started? It's confusing how the question tells you the speed of the bullet but then says the speed isn't known.

 

[hypermorphism]

I would start with the fact that you know the potential energy of the compressed spring, and since no other information is given, you can assume that all the kinetic energy of the bullet and block was used in compressing the spring. Can you get started from here ?

 

[stunner5000pt]

you have to use BOTH conservation of momentum and energy

along came a bullet of some momentum. I'm sure the bullet embeds itself into the block. SO after the bullet struck the block, they both have some common velocity. ow for the energy part.
The velocity has some associated kinetic energy, which was all converted into the spring's energy. Form the relations based on this

 

[Nenad]

Just feeling like solving it, the answer is 435.9m/s. Justdo what the guyes befoure me told you to do. All you need is:
$$PE_{spring} = \frac{1}{2}kx^2$$
$$KE_{system} = \frac{1}{2} (m_{bullet} + m_{block})v_{system}^2$$
Very simple.

Regards,

Nenad