Final answer:
To arrive at the same point after driving 7.50 km in a direction 15° east of north, you would need to drive approximately 2.12 km east and 7.12 km north. Reversing the order of the east and north legs would still result in arriving at the same point.
Step-by-step explanation:
To find the distances you would have to drive straight east and then straight north to arrive at the same point, you can use trigonometry. Since the original displacement is 7.50 km in a direction 15° east of north, you can find the east and north components of the displacement by using sine and cosine.
The east component of the displacement is given by:
east component = displacement * sin(angle)
east component = 7.50 km * sin(15°)
The north component of the displacement is given by:
north component = displacement * cos(angle)
north component = 7.50 km * cos(15°)
Therefore, the distances you would have to drive straight east and then straight north to arrive at the same point are approximately 2.12 km east and 7.12 km north.
If you reverse the order of the east and north legs, you would still arrive at the same point. This is because the overall displacement remains the same, regardless of the order of the legs.