A 30-g bullet is fired with a horizontal velocity of 450 m/s and becomes embedded in block B which has a mass of 3 kg. After the impact, block B slides on a 30-kg carrier C until it impacts the end of the carrier. Knowing the impact between B and C is perfectly plastic determine (a) velocity of the bullet and B after the first impact, (b) the final velocity of the carrier (Distance between C and B is 0.5 m)

a.) 4.46 m/s

b.) 0.41 m/s

Explanation:

a) Given that the mass M of the bullet = 30g = 30/1000 = 0.03 kg

Velocity V = 450 m/s

From conservative of linear momentum,

Sum of momentum before impact = Sum of momentum after impact

0.03 × 450 = (0.03 + 3 ) × v₂

v₂ = 13.5/3.03 = 4.4554 m/s

Therefore the velocity of the bullet and B after the first impact = 4.46 m/s approximately

(b) To calculate the velocity of the carrier, you will consider the conservation of linear momentum again.

(m₁ + m₂)×v₂  = (m₁ + m₂ + m₃)×v₃

Where:

Mass of the carrier m₃ = 30 kg

Substitute all the parameters into the formula

3.03×4.4554 = (3.03 +30) × v₃

v₃ = 13.5 / 33.03 = 0.40872 m/s

Therefore the velocity of the carrier is 0.41 m/s approximately.

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