Final answer:
A hiker's average speed, average velocity, and instantaneous velocity for different legs of a hike are calculated based on given distance and time.
Step-by-step explanation:
A) Average speed for hike: To find the average speed, we need to calculate the total distance traveled and divide it by the total time taken. The hiker walks 15 km north in 5 hours, turns around and walks 3 km south in 1 hour, and finally turns around and walks 2 km north in 2 hours. The total distance traveled is 15 km + 3 km + 2 km = 20 km. The total time taken is 5 hours + 1 hour + 2 hours = 8 hours. So, the average speed for the hike is 20 km / 8 hours = 2.5 km/hr.
B) Average velocity for hike: Average velocity takes into account the direction of motion. Since the hiker starts and ends at the same point, the total displacement is zero. Therefore, the average velocity for the hike is also zero.
C) Instantaneous velocity for 1st leg of hike: Instantaneous velocity is the velocity at a specific point in time. Since the hiker walks 15 km north in 5 hours, the instantaneous velocity for the 1st leg of the hike can be calculated by dividing the displacement of 15 km by the time of 5 hours. Therefore, the instantaneous velocity for the 1st leg of the hike is 15 km / 5 hours = 3 km/hr.