A 306-kg car moving at 16.5 m/s hits from behind a 810-kg car moving at 13.2 m/s in the same direction. If the new speed of the heavier car is 17.5 m/s, what is the velocity of the lighter car after the collision, assuming that any unbalanced forces on the system are negligibly small?

v₂f = 5.1 m/s

Explanation:

Assuming no external forces acting during the collision, total momentum must be conserved.⇒ p₀ = pfThe initial momentum p₀, can be written as follows:

       

       where m₁ = 306 kg, m₂ = 810 kg, v₁₀ = 16.5 m/s, v₂₀ = 13.2 m/s

The final momentum, pf, can be written as follows:

       

        where v₂f = 17.5 m/s

Since p₀ = pf, which means that (1) is equal to (2),Replacing by the givens, and rearranging, we can solve for the only unknown that still remains, v₁f, as follows:

       

The velocity of the lighter car after the collision is 5.1 m/s.

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