A projectile (mass = 0.10 kg) is fired at and embeds itself in a target (mass = 2.11 kg). The target (with the projectile in it) flies off after being struck. What percentage of the projectile's incident kinetic energy does the target (with the projectile in it) carry off after being struck?

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To calculate the percentage of the projectile's incident kinetic energy carried off by the target, we need to consider the conservation of momentum.

The principle of conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. In this case, we can assume that no external forces are acting on the system (projectile + target).

The momentum of an object is given by the product of its mass and velocity. So, we can write the momentum conservation equation as:

(initial momentum of the projectile) = (final momentum of the projectile) + (final momentum of the target)

Since the projectile embeds itself into the target, it comes to rest after the collision. Therefore, the final velocity of the projectile is zero.

The initial momentum of the projectile can be calculated using its mass and initial velocity, while the final momentum of the target can be calculated using its mass and final velocity.

The initial kinetic energy of the projectile is given by the formula:

(initial kinetic energy of the projectile) = 0.5 * (mass of the projectile) * (initial velocity of the projectile)^2

The final kinetic energy of the target is given by the formula:

(final kinetic energy of the target) = 0.5 * (mass of the target) * (final velocity of the target)^2

To find the final velocity of the target, we can rearrange the momentum conservation equation:

(final momentum of the target) = (initial momentum of the projectile) - (final momentum of the projectile)

Since final momentum of the projectile is zero, we can simplify the equation:

(final momentum of the target) = (initial momentum of the projectile)

From here, we can solve for the final velocity of the target:

(final velocity of the target) = (initial momentum of the projectile) / (mass of the target)

Finally, we can substitute the final velocity of the target into the formula for final kinetic energy of the target to get its value.

Once we have the initial kinetic energy of the projectile and the final kinetic energy of the target, we can calculate the percentage of the projectile's incident kinetic energy carried off by the target using the following formula:

(percentage of kinetic energy carried off) = (final kinetic energy of the target) / (initial kinetic energy of the projectile) * 100

Plugging in the given values and following these steps will give you the desired percentage.