A 16.0 g bullet is fired horizontally into a 87 g wooden block that is initially at rest on a frictionless horizontal surface and connected to a spring having spring constant 168 N/m. The bullet becomes embedded in the block. The bullet block system compresses the spring by a maximum of 1.30 cm. (a) What is the velocity of the block once the bullet is imbedded?

To find the velocity of the block once the bullet is embedded, we can use the principle of conservation of momentum. The initial momentum of the bullet, before it hits the block, is equal to the final momentum of the bullet-block system after the collision.

The momentum of an object is given by the product of its mass and velocity.

Let's calculate the initial momentum of the bullet and the final momentum of the bullet-block system.

1. Initial momentum of the bullet:
The mass of the bullet is given as 16.0 g, which is equivalent to 0.016 kg.
Since the bullet is fired horizontally, its initial velocity can be considered as the speed of the bullet before impact with the block.

2. Final momentum of the bullet-block system:
Since the bullet becomes embedded in the block, the mass of the bullet and the block together will be considered as the mass of the system.
The combined mass is the sum of the mass of the bullet (0.016 kg) and the mass of the wooden block (87 g), which is equivalent to 0.087 kg.

Now, we can write the conservation of momentum equation:

(initial momentum of bullet) = (final momentum of bullet-block system)

(mass of bullet) x (initial velocity of bullet) = (mass of system) x (final velocity of system)

0.016 kg x (initial velocity of bullet) = 0.087 kg x (final velocity of system)

Now, let's solve for the final velocity of the system:

final velocity of system = (0.016 kg x initial velocity of bullet) / 0.087 kg

To calculate the initial velocity of the bullet, we need more information or data provided in the problem. Please provide the initial velocity of the bullet so we can calculate the final velocity of the block once the bullet is embedded.