A Runner Jogs 12km North Then Turns And 16km East in Three Hours.1 What Is His Displacement? 2 Calculate His Average Speed 3 Calculate His Average Velocity(including The Direction)

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36.9 To find the runner's displacement, average speed, and average velocity, we need to break down the problem step by step.

1. Displacement: Displacement is the change in position of an object. To find the runner's displacement, we need to calculate the distance and direction of the straight line between the starting point and the ending point.

In this case, the runner first jogs 12 km north, then turns and runs 16 km east. We can represent these movements on a coordinate plane, where north is the positive y-axis and east is the positive x-axis.

Using the Pythagorean theorem, we can calculate the displacement as follows:
Displacement = √(12^2 + 16^2) = √(144 + 256) = √400 = 20 km

So, the runner's displacement is 20 km.

2. Average Speed: Average speed is the total distance traveled divided by the total time taken. In this case, the runner jogs 12 km north and then runs 16 km east in 3 hours.

Total distance = 12 km + 16 km = 28 km
Total time = 3 hours

Average Speed = Total distance / Total time = 28 km / 3 hours ≈ 9.33 km/h

So, the runner's average speed is approximately 9.33 km/h.

3. Average Velocity: Average velocity is the displacement of an object divided by the total time taken. It includes both the magnitude (distance) and the direction.

Using the displacement we calculated earlier (20 km) and the total time taken (3 hours), we can calculate the average velocity as follows:
Average Velocity = Displacement / Total time = 20 km / 3 hours ≈ 6.67 km/h

Since the runner jogged north and then turned and ran east, we need to consider the direction. We can represent this using a vector notation. The runner's average velocity can be represented as 6.67 km/h north-east.

So, the runner's average velocity is approximately 6.67 km/h north-east.