A 2.50 g bullet, traveling at a speed of 485 m/s, strikes the wooden block of a ballistic pendulum, such as that in the figure below. The block has a mass of 275 g.

To find the answer to your question, we need to determine the velocity of the block after the bullet strikes it. We can start by applying the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Let's denote the velocity of the bullet before the collision as V_bullet, the velocity of the block after the collision as V_block, the mass of the bullet as m_bullet, and the mass of the block as m_block.

The momentum of an object is given by the product of its mass and velocity. Therefore, the initial momentum of the system (bullet + block) before the collision is:

Initial momentum = momentum of the bullet + momentum of the block

Initial momentum = m_bullet * V_bullet + m_block * 0 (since the block is initially at rest)

After the bullet strikes the block, they move together as one system. So, the final momentum of the system is:

Final momentum = (m_bullet + m_block) * V_block

Since the principle of conservation of momentum states that the initial momentum is equal to the final momentum, we can equate these two expressions:

m_bullet * V_bullet + m_block * 0 = (m_bullet + m_block) * V_block

Now, we can plug in the given values to solve for V_block:

m_bullet = 2.50 g = 0.0025 kg
V_bullet = 485 m/s
m_block = 275 g = 0.275 kg

0.0025 kg * 485 m/s + 0.275 kg * 0 = (0.0025 kg + 0.275 kg) * V_block

1.2125 kg m/s = 0.2775 kg * V_block

Dividing both sides by 0.2775 kg, we find:

1.2125 kg m/s / 0.2775 kg = V_block

V_block = 4.37 m/s

Therefore, the velocity of the block after the bullet strikes it is 4.37 m/s.

To solve this problem, we need to find the final velocity of the block after the bullet strikes it. We can use the principle of conservation of momentum to solve for the final velocity.

Step 1: Find the momentum of the bullet.
Momentum (p) = mass (m) x velocity (v)
p_bullet = (2.50 g) x (485 m/s)

Step 2: Find the momentum of the block before the collision.
The block is initially at rest, so its momentum is zero.

Step 3: Find the total momentum after the collision.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
p_total_before = p_bullet
p_total_after = p_bullet + p_block

Step 4: Solve for the final velocity of the block.
p_total_before = p_total_after
p_bullet = p_bullet + p_block

Now let's substitute the values and solve:
(2.50 g) x (485 m/s) = p_bullet + (275 g) x (v_final)

Step 5: Convert the masses to kilograms.
1 g = 0.001 kg
So, the bullet mass becomes 2.50 g x 0.001 kg/g = 0.0025 kg
And the block mass becomes 275 g x 0.001 kg/g = 0.275 kg

Now let's substitute the values again:
(0.0025 kg) x (485 m/s) = 0.0025 kg x (v_final) + (0.275 kg) x (v_final)

Step 6: Solve for the final velocity of the block.
0.0025 kg x 485 m/s = 0.0025 kg x v_final + 0.275 kg x v_final

Step 7: Combine like terms.
1.2125 kg·m/s = (0.0025 kg + 0.275 kg) x v_final

Step 8: Calculate the sum of the masses.
0.0025 kg + 0.275 kg = 0.2775 kg

Now let's substitute the values again:
1.2125 kg·m/s = 0.2775 kg x v_final

Step 9: Solve for the final velocity of the block.
v_final = 1.2125 kg·m/s / 0.2775 kg

Step 10: Calculate the final velocity.
v_final ≈ 4.37 m/s

Therefore, the final velocity of the wooden block after the bullet strikes it is approximately 4.37 m/s.