A projectile (mass = 0.17 kg) is fired at and embeds itself in a target (mass = 2.84 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?
Incorrect: Your answer is incorrect. %
To find the percentage of the projectile's incident kinetic energy carried off by the target, we need to compare the kinetic energy before and after the impact.
1. Calculate the initial kinetic energy of the projectile:
The kinetic energy of an object is given by the formula:
KE = 0.5 * mass * velocity^2
Given:
- Mass of the projectile (m1) = 0.17 kg
- Velocity of the projectile before impact (v1) = ?? (not specified in the question)
2. Calculate the kinetic energy of the combined system (projectile embedded in the target) after impact:
To do this, we need to determine the final velocity of the combined system after impact.
Let v2 be the final velocity of the combined system after impact.
Since the target is initially at rest, the total momentum before and after the impact is conserved:
m1 * v1 = (m1 + m2) * v2
Rearranging the equation, we can solve for v2:
v2 = (m1 * v1) / (m1 + m2)
3. Calculate the final kinetic energy of the combined system:
The final kinetic energy is given by:
KE = 0.5 * (m1 + m2) * v2^2
4. Calculate the percentage of the projectile's incident kinetic energy carried off by the target:
Percentage carried off = (Final kinetic energy / Initial kinetic energy) * 100
Since the question does not provide the velocity of the projectile before impact (v1), it is not possible to calculate the correct answer without further information. Please ensure all necessary information is provided to find the correct answer.