Question

A boy runs 800m northwards, followed by 600m westwards. What is the magnitude of his distance and displacement ?

I want to know how to solve it in steps..

Answer 1

`1000` meters in the northwest direction.

Explanation:

For this problem, I will draw a diagram to make things easier to visualize.

Let `S` be the starting position of the boy.

Then, we know that the boy walks `800` meters north, so we draw a point, let's call it `A`, and the north line `SA` will be `800` meters long. For convenience, I'll make a scale factor of `100` times smaller to make it easier to draw.

After that, we know that the boy walks `600` meters in the west direction, so we construct another point, let's say `B`, perpendicular to the line `AS`, i.e. `AB_|_AS` at `A`.

The total displacement is the shortest route from the boy's current position, `B` from his original position, which is `S`. From here, we see a right triangle, `DeltaSAB`.

So, the total displacement will be the line `SB`. Using Pythagoras's theorem, we get as follows:

`SB^2=AB^2+AS^2`

`=8^2+6^2`

`=64+36`

`=100`

`:.SB=sqrt(100)=10`, since `SB>0`.

Since the scale is `100x` smaller, the real distance would be `10*100=1000` meters.

From here, we can also see that the boy has moved in the northwest direction from his original position, so we say that the total displacement is `1000` meters northwest.