Question

A car of mass 1000 kg travelling at 15 m/s crashes into the back of a second car of mass 800 kg which was travelling at 5 m/s in the same direction. The cars lock together after the collision. What velocity do the cars move off with?

Answer 1

Using the conservation of momentum, the velocity of the two cars after the collision, where they move off locked together, is calculated to be 10.56 m/s.

Step-by-step explanation:

To find the velocity of the cars after they lock together in a collision, we can use the conservation of momentum, which states that the total momentum before the collision must be equal to the total momentum after the collision. Given a first car with a mass of 1000 kg traveling at 15 m/s and a second car with a mass of 800 kg traveling at 5 m/s, the combined mass after collision is 1000 kg + 800 kg = 1800 kg. We can set up the equation as follows:

m1 ∙ v1 + m2 ∙ v2 = (m1 + m2) ∙ v_final

1000 kg ∙ 15 m/s + 800 kg ∙ 5 m/s = 1800 kg ∙ v_final

Solving for v_final gives us:

v_final = (1000 ∙ 15 + 800 ∙ 5) / 1800

15000 kg∙m/s + 4000 kg∙m/s = 19000 kg∙m/s

19000 kg∙m/s / 1800 kg = 10.56 m/s

Therefore, the velocity of the two cars moving together after the collision is 10.56 m/s.