Question

A projectile (mass = 0.25 kg) is fired at and embeds itself in a stationary target (mass = 2.28 kg). With what percentage of the projectile's incident kinetic energy does the target (with the projectile in it) fly off after being struck?

Answer 1

Let the Initial velocity of the projectile = u
Mass of projectile, m = 0.25 kg
Mass of target, M = 2.28 kg

Let the final velocity of the system be v.
Mass of the system = m + M = 2.53 kg

Apply the Principle Of Conservation of Momentum :
mu + 0 = (m + M)v
v = mu / (m + M)

Initial K.E. of the system = K.E. of projectile + K.E. of target = 1/2*mu^2 + 0 = 1/2*mu^2
Final K.E. of the system = 1/2*(m + M) v^2 = 1/2*m^2*u^2 / (m + M)

% of KE carried by the system = KE of system / KE of projectile * 100
= 100m / (m + M) = 9.88 %