# A hiker travels 300 m [N], turns around and hikes 550 m [S], and then hikes back another 50.0 m[N]. He manages to do this in 7200 seconds. What is the hiker's displacement? What is the hiker's average speed? What is the hiker's velocity?

Jul 20, 2015

Displacement: 200 m
Average speed: 0.125 m/s
Average velocity: 0.0278 m/s

#### Explanation:

Let's start with the hiker's displacemnt, which is simply the distance between its starting point and its finish point.

Displacement does not take into account the path taken from start to finish, it just deals with the shortest distance between these two points.

So, you know that your hiker first travels 300 m north, then turns around and hikes 550 m south.

At this point, he will be 250 m south of his starting point, since hiking 300 m south would have taken him right back to his starting point.

After this, he walks 50 m north again, towards the starting point.

This means that the distance between the starting point and the finish point will be equal to 200 m. The hiker's displacement will thus be

d_"hiker" = color(green)("200 m")

Now for his average speed. Average speed is defined as the total distance covered by the hiker divided by the time total time needed to cover this distance.

The total distance covered by the hiker will be

${d}_{\text{total" = 300 + 550 + 50 = "900 m}}$

This means that his average speed was

v_"avg" = d_"total"/t_"total" = "900 m"/"7200 s" = color(green)("0.125 m/s")

Velocity is actually a vector quantity, so you need to determine both the magnitude and the direction of the vector.

Because your hiker changes direction, you can't have a constant velocity. This means that you have to use average velocity, which, for straight line motions, is simply the ratio between the displacement of the hiker and the total time of the motion.

bar(v) = d/t_"total" = "200 m"/"7200 s" = color(green)("0.0278 m/s")