Final answer:
The man's average speed for the trip is 6.5 mph, and his average velocity is 0.5 mph south. None of the provided options are correct. The man's speed differs because you need to consider the total distance traveled, and his velocity differs as it is the displacement over time.
Step-by-step explanation:
The question requires calculating the average speed and average velocity of a man who walked in various directions, totaling a certain distance over a 2-hour period. To calculate the speed, we take the sum of all distances traveled regardless of direction, and divide by the total time. To calculate velocity, we consider displacement, which is the straight-line distance from the starting point to the ending point in a specific direction, divided by the total time.
First, we calculate the total distance traveled:
2 miles (North) + 4 miles (East) + 4 miles (West) + 3 miles (South) = 13 miles
The trip took 2 hours, so:
Average speed = Total distance traveled / Total time
Average speed = 13 miles / 2 hours = 6.5 mph.
Next, to find the displacement, we note that his final position is 2 miles north plus 3 miles south, which is 1 mile south, and 4 miles east minus 4 miles west, which is 0 miles east-west. Hence, the total displacement is 1 mile south over 2 hours.
Average velocity = Displacement / Total time
Since the man ended up 1 mile away from his starting point after 2 hours due south, we have:
Average velocity = 1 mile south / 2 hours = 0.5 mph south.
None of the given options (A, B, C, or D) match our calculations. The correct answer should be Speed: 6.5 mph, Velocity: 0.5 mph south.