A bullet with a mass mb=13.5 g is fired into a block of wood at velocity vb=245 m/s. The block is attached to a spring that has a spring constant k of 205 N/m. The block and bullet continue to move, compressing the spring by 35.0 cm before the whole system momentarily comes to a stop. Assuming that the surface on which the block is resting is frictionless, determine the mass mw of the wooden block.

Momentum is conserved, so the sum of the momenta of the bullet and block before collision is equal to the momentum of the combined bullet-block system,

where v is the speed of the bullet-block system. The block starts at rest so it has no initial momentum, and solving for v gives

The total work W performed by the spring on the bullet-block system as it is compressed a distance x is

where k is the spring constant, and the work done is negative because the restoring force of the spring opposes the bullet-block as it compresses the spring.

By the work-energy theorem, the total work done is equal to the change in the bullet-block's kinetic energy ∆K, so we have

The bullet-block starts moving with velocity v found earlier and comes to a stop as the spring slows it down, so we have

Solve for :

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

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