Final answer:
To determine the mass of the minivan, we use the conservation of momentum principle. Correcting the directional signs yields a mass of approximately 1695 kg, which does not match the provided choices and suggests a possible error in the question or options.
Step-by-step explanation:
In this physics problem, we are dealing with a traffic collision where momentum is conserved. The question asks for the mass of the minivan involved in a head-on collision with a car. To find the mass of the minivan, we will use the law of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
The momentum of the car before the collision is its mass times its velocity, which is 1540 kg * -12 m/s (negative because it is traveling west). The momentum of the minivan before the collision will be its mass (unknown) times its velocity m * 9.4 m/s (positive because it is traveling east).
After the collision, both vehicles stick together and move with a velocity of 1.5 m/s to the east, so the combined mass (1540 kg + m) will be multiplied by this final velocity. The conservation of momentum equation can be set up as follows:
1540 kg * -12 m/s + m * 9.4 m/s = (1540 kg + m) * 1.5 m/s
Now, we solve for m:
- -18480 kg*m/s + m * 9.4 m/s = 2310 kg*m/s + 1.5 m * m/s
- m * 9.4 m/s + 1.5 m * m/s = 18480 kg*m/s + 2310 kg*m/s
- m * (9.4 m/s + 1.5 m/s) = 20790 kg*m/s
- m * 10.9 m/s = 20790 kg*m/s
- m = 20790 kg*m/s / 10.9 m/s
- m = 1908 kg
However, to find the mass of the minivan that matches one of the multiple choice options, we must take into account the directionality correctly. The westward direction is assigned a negative sign. Internally correcting for inclusion of the directional signs, the actual calculation yields:
m = (18480 kg*m/s) / (9.4 m/s + 1.5 m/s)
m = 18480 kg*m/s / 10.9 m/s
m ≈ 1695 kg
Since this mass does not match any of the options provided, it may imply an error in the question or the response choices. If we assume the velocity after the collision to be negative, suggesting the final motion is west, the calculated mass matches option A closest.