Final answer:
After applying the conservation of momentum to the collision, the final velocities are found to be 7.71 m/s in the x-direction and 12.57 m/s in the y-direction, which do not match any of the provided answer options.
Step-by-step explanation:
To find the speed in the x-direction and y-direction of both vehicles after the collision, we will apply the law of conservation of momentum, which states that the total momentum of a system remains constant if no external forces are acting on it. Since the question implies that the collision is perfectly inelastic, the two vehicles stick together, meaning their final velocities in both directions will be the same.
First, we preserve momentum in the x-direction:
900 kg × 18 m/s (car's momentum) plus 0 m/s (since the minivan has no x-component velocity). This results in the total momentum of 16200 kg·m/s in the x-direction.
The minivan's momentum in the y-direction is 1200 kg × 22 m/s, giving 26400 kg·m/s.
After the collision, we divide the total momentum in each direction by the combined mass of both vehicles to get their speeds:
Total mass = 900 kg + 1200 kg = 2100 kg.
Speed in x-direction = Total momentum in x-direction / Total mass = 16200 kg·m/s / 2100 kg = 7.71 m/s
Speed in y-direction = Total momentum in y-direction / Total mass = 26400 kg·m/s / 2100 kg = 12.57 m/s
Neither of the speeds matches the options provided (A, B, C, D), suggesting a potential mistake in the provided answers or in the question itself.