Question

Car A runs a red light and broadsides Car B, which is stopped and waiting to make a left turn. Car A has a mass of 1,800 kg. Car B has a mass of 1,500 kg. After the impact, the cars stick together and slide away at a speed of 7.1m/s. How fast was Car A going when it hit Car B? Can someone explain the steps to find the answer please?

Answer 1

13 m/s

Step-by-step explanation:

Momentum is conserved, so initial total momentum = final total momentum.

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

Since Car B is originally not moving, u₂ = 0.

m₁ u₁ = m₁ v₁ + m₂ v₂

Since the cars stick together, they have the same final velocity, so v₁ = v₂ = v.

m₁ u₁ = m₁ v + m₂ v

m₁ u₁ = (m₁ + m₂) v

Given that m₁ = 1800, m₂ = 1500, and v = 7.1:

1800 u₁ = (1800 + 1500) 7.1

u₁ = 13

Car A was travelling at 13 m/s.