What percentage of the projectile's incident kinetic energy does the target (with the projectile in it) carry

Question

A projectile (mass = 0.20 kg) is fired at and embeds itself in a target (mass = 2.50 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?
______%

Answer 1

conservation of momentum states that
v1*.2=2.7*v2
v2=v1*.2/2.7

the question asked to compare starting with ending kinetic (energy is not conserved)
.5*.2*v1^2 is starting

.5*2.7*v2^2 is ending

the % is
(2.7*v2^2/(.2*v1^2))*100%


substituting in from the momentum
2.7*(v1*.2/2.7)^2/(.2*v1^2)*100%
or
(.2/2.7)*100%

note that this is the ratio of the masses
=7.4 %

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