A 2.0 kg mass moving at 5.0 m/s suddenly collides head-on with a 3.0 kg mass at rest. If the collision is perfectly inelastic, how much kinetic energy was lost during the collision? (a) 20 J
(b) 26 J
(c) 15 J
(d) 8 J

correct answer is (c) 15 J

Explanation:

given data

mass m1 = 2 kg

velocity V1 = 5 m/s

mass other  = 3 kg

so mass m2 = 2+ 3 kg = 5 kg

solution

we will apply here conservation of momentum:

m1V1 = m2V2  1

put here value and we get  velocity v2

(2.0) × (5.0) = (2.0 + 3.0) × V

solve it we get

10 = 5 × V 2

V2 = 2.0 m/s

so here kinetic energy will be

KE = ½ × m × v²

so

∆KE = ½ × m1 × (v1)²  -  ½  × m2 × (v2) ²

∆KE = 0.5 × 2 × 25 - 0.5 × 5 × 4

 ∆KE = 25 - 10

∆KE  = 15 J