A bullet of mass 8 g strikes a ballistic pendulum of mass 2.0 kg. The center of mass of the pendulum rises a vertical distance of 10 cm. Assuming that the bullet remains embedded in the pendulum, calculate the bullet's initial speed.

The momentum of the bullet: massbullet*velocity

that has to equal the momentum of the block and bullet combination at impact(mblock+massbullet)V set them equal, and solve for V.

Now, the initialKE of the block and bullet combination is 1/2 (totalmass)V^2
set that equal to the change in PEnergy
totalmass*g*height.

solve for height in terms of initial bullet velocity.

WEll, you know height, so you can solve for bullet velocity.

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To calculate the bullet's initial speed, we can use the principle of conservation of linear momentum and the principle of conservation of energy.

1. Start by calculating the initial momentum of the bullet before it strikes the pendulum. Momentum is calculated as the product of mass and velocity (P = m * v). The mass of the bullet is 8 g, which is equal to 0.008 kg.

2. Since the bullet is embedded in the pendulum, the combined mass of the bullet and pendulum after the collision is the sum of their individual masses. The mass of the pendulum is 2.0 kg, which brings the total mass to 2.008 kg.

3. The conservation of linear momentum states that the total momentum before the collision is equal to the total momentum after the collision. Therefore, the initial momentum of the bullet is equal to the final momentum of the pendulum after the collision.

4. After the collision, the pendulum rises a vertical distance of 10 cm, which is equal to 0.1 m. This rise in height implies a gain in potential energy for the pendulum.

5. Using the principle of conservation of energy, the change in potential energy of the pendulum is equal to the initial kinetic energy of the bullet. The potential energy of an object mass m at height h is given by the formula: PE = m * g * h, where g is the acceleration due to gravity (9.8 m/s^2).

6. Set up the equation for conservation of energy: m * g * h = (1/2) * m * v^2, where v is the initial velocity of the bullet.

7. Substitute the known values into the equation: 0.008 kg * 9.8 m/s^2 * 0.1 m = (1/2) * 0.008 kg * v^2.

8. Simplify the equation: 0.008 kg * 0.98 m^2/s^2 = 0.004 kg * v^2.

9. Solve for v^2: v^2 = (0.008 kg * 0.98 m^2/s^2) / 0.004 kg = 0.196 m^2/s^2.

10. Take the square root of both sides to find v, the initial velocity of the bullet: v = sqrt(0.196 m^2/s^2) = 0.44 m/s.

Therefore, the bullet's initial speed is 0.44 m/s.