Question

An athlete runs 9km due east, then 18km north and finally 5km west. What is the total distance run? What is the resulting displacement of the hiker from the starting point?

Answer 1

Distance: 32 km

Displacement: 18 km

Step-by-step explanation:

Distance is the total amount travelled. Displacement on the other hand is how far away an object is from its starting point.

Distance is a scalar quantity meaning it only has magnitude. Displacement is a vector quantity meaning it has magnitude and direction.

Distance is represented by "x" while displacement is represented as "Δx".

Note that "Δ" is the Greek letter "delta" which is used to represent a change in something.

Let's start by finding the distance.

Since distance is the total amount travelled, we can just add all of the values.

9km + 18km + 5km = 32 km

Then, we can find the displacement.

North and East are positive while South and West are negative.

If the athlete ran 9km East and 5km West, their displacement would be:

9km - 5km = 4km East

Now, we can set up a triangle to determine the displacement from the starting point.

18km North would be the longer leg, 4km East would be the shorter leg, and the displacement would be the hypotenuse.

Using Pythagorean's Theorem we find that:

`a^2+b^2=c^2\\4^2+18^2=c^2\\16+324=c^2\\340=c^2\\c\approx18`

Note that "a" and "b" represent the legs of the triangle while "c" represents the hypotenuse of the triangle.

The displacement is approximately 18m.