Question

A projectile (mass = 0.30 kg) is fired at and embeds itself in a stationary target (mass = 2.15 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 = 0.3 kg

Mass of target, M = 2.15 kg

Let the final velocity of the system be v.

Mass of the system = m + M = 2.45 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) = 12.24 %