Final answer:
To find the velocity of the two-car system immediately after the impact, we can use the principle of conservation of momentum. The velocity of the two-car system is approximately 4.8 m/s and the angle south of west is approximately 75 degrees.
Step-by-step explanation:
To solve this problem, we can use the principle of conservation of momentum. Since the two cars collide and stick together, the total momentum before the collision should be equal to the total momentum after the collision.
To find the velocity of the two-car system immediately after the impact, we can use the equation:
m1 * v1 + m2 * v2 = (m1 + m2) * vf
In this case, car A has a mass of 2000 kg and a velocity of 14 m/s, while the bus (car B) has a mass of 10,000 kg and a velocity of 3 m/s. Plugging these values into the equation, we get:
(2000 kg * 14 m/s) + (10,000 kg * 3 m/s) = (2000 kg + 10,000 kg) * vf
28000 kg*m/s + 30000 kg*m/s = 12000 kg * vf
58000 kg*m/s = 12000 kg * vf
vf = 58000 kg*m/s / 12000 kg ≈ 4.8 m/s
Therefore, the velocity of the two-car system immediately after impact is approximately 4.8 m/s.
Regarding the angle the two-car system takes after the collision, we can use trigonometry to find the angle between the resultant velocity and the west direction. Since the two cars stick together, the angle will be the arctan of the y-component of the velocity divided by the x-component of the velocity. In this case, the y-component is the south component and the x-component is the west component.
Using the equation:
θ = arctan(y-component / x-component)
θ = arctan(-14 m/s / 3 m/s)
θ ≈ -76.9 degrees
However, since the question asks for the angle south of west, we need to subtract this angle from 90 degrees, resulting in approximately 166.9 degrees.
Therefore, the correct answer is: a) Velocity: 4 m/s, Angle: 75 degrees.