A1250 kg car is moving down the highway with a velocity of 32.0 m/s when it bumps into the car ahead of it which has a mass of 875 kg and a velocity of 25.0 m/s. after the collision, the two cars stick together. what will be the resulting velocity of the two cars together? how much energy will be lost in this collision?

Resulting velocity = 29.1 m/s

Lost energy = 13701.875 j ≈ 13702 j

The collision is elastic so, the final velocity of the car will be the same. Therefore,

v = m₁v₁ + m₂v₂/m₁ + m₂

v = final velocity

m₁ = mass of car1 = 1250 kg

m₂ = mass of car2 = 875 kg

v₁ = initial velocity of car1  = 32 m/s

v₂ = initial velocity of car2 = 25 m/s

v = (1250×32) + (875×25)/ 1250 + 875

v = 40000 + 21875/2125

v = 61875 / 2125

v = 29.1176470588 ≈ 29.1m/s

Let's calculate the lost kinetic energy.

The before kinetic energy will  be

KE₁ + KE₂ = total KE

KE₁  =1/2×1250×32²= 640000 j

KE₂ = 1/2 × 875 × 25²  = 273437.5  j

total = 640000 j + 273437.5  j = 913437.5 j

After kinetic energy

1/2×(1250+875)×29.1² = 899735.625 j

Lost energy  = 913437.5 j -  899735.625 j = 13701.875 j ≈ 13702 j

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