Question

Car A runs a red light and crashes into Car B, which is waiting to make a left turn. Car A has a mass of 2,000 kg. Car B has a mass of 1,500 kg. After the impact, the cars stick together and slide away at a speed of 9.1m/s. How fast was Car A going when it hit Car B? Show all of your work. (Law of Conservation of Momentum) ​

Answer 1

Using the Law of Conservation of Momentum, we calculate that Car A was going approximately 15.93 m/s when it collided with Car B, given that both cars stuck together and slid away at 9.1 m/s post-collision.

Step-by-step explanation:

To determine how fast Car A was going when it hit Car B, we'll use the Law of Conservation of Momentum. The total momentum of a system is conserved if no external forces act on it. Since Car B was waiting to make a left turn, its velocity was 0 m/s. After the collision, both cars moved together with a combined mass of 3500 kg (2000 kg + 1500 kg) at a velocity of 9.1 m/s.

The total momentum before the collision (p_initial) must equal the total momentum after the collision (p_final):

p_initial = p_final

The momentum of Car A before the collision is m_A * v_A, and the momentum of Car B is m_B * v_B (which is 0 since Car B is stationary). After the collision, the momentum is (m_A + m_B) * v_final.

Setting the initial and final momentum equal:

m_A * v_A + m_B * v_B = (m_A + m_B) * v_final

2000 kg * v_A + 0 = 3500 kg * 9.1 m/s

Therefore, v_A = (3500 kg * 9.1 m/s) / 2000 kg

v_A = 15.925 m/s

So, Car A was going approximately 15.93 m/s when it collided with Car B.

Answer 2

The law of conservation of momentum tells us that momentum is conserved, therefore total initial momentum should be equal to total final momentum. In this case, we can expressed this mathematically as:

mA vA + mB vB = m v

where, m is the mass in kg, v is the velocity in m/s

since m is the total mass, m = mA + mB, we can write the equation as:

mA vA + mB vB = (mA + mB) v

furthermore, car B was at a stop signal therefore vB = 0, hence

mA vA + 0 = (mA + mB) v

1800 (vA) = (1800 + 1500) (7.1 m/s)

vA = 13.02 m/s

Step-by-step explanation: