Final answer:
The net momentum of the two vehicles approaching the intersection has an x-component of -33800 kg·m/s and a y-component of 28600 kg·m/s, with the resulting direction in the northwest quadrant given the negative x (west) and positive y (north) directions.
Step-by-step explanation:
To determine the direction of the net momentum of the two vehicles approaching the intersection, we must consider the momentum vectors for each car. Since momentum is a vector quantity, we can calculate the momentum of each vehicle along the x-axis (east-west) and y-axis (south-north) and then use these to find the resultant vector.
The pickup has a mass of 2600 kg and a velocity of -13.0 m/s (since it's traveling from east to west, we consider the negative direction). Its momentum along the x-axis (px) is:
px = mass × velocity = 2600 kg × -13.0 m/s = -33800 kg·m/s
The sedan has a mass of 1300 kg and is moving at 22.0 m/s to the north, along the y-axis. Its momentum (py) is:
py = mass × velocity = 1300 kg × 22.0 m/s = 28600 kg·m/s
The net momentum vector is obtained by combining these two momentum vectors. Graphically, this can be represented with a right-angled triangle, where the x-axis vector points left and the y-axis vector points up. Using the Pythagorean theorem, we can calculate the magnitude of the resultant vector.
To find the direction, we use the arctan function:
direction = arctan(py / px)
In this case:
direction = arctan(28600 / -33800) which will give us an angle in the northwest quadrant, since the x-component is negative and the y-component is positive. Remember to adjust the angle using the appropriate reference angle if you are using a basic calculator that does not consider quadrants.