Question

A girl rode a scooter 43 m north, then 38 m south, and then 16 m north. The girl then rode south again before stopping. Her total distance traveled was 122 m. How far south did she ride on the last part of her trip, and what was her total displacement

Answer 1

Answer:

First, let's write some definitions.

Displacement is the distance between the final position and the initial position.

Here we can define north as the positive direction and south as the negative one.

First, we assume that the initial position is 0m

We know that she first goes 43m north

Then she goes 38m south

Then she goes 16m north

And then she goes south again for X meters, such that the total distance traveled is 122m

The total distance traveled is the sum of all distances traveled, regardless of the direction

then we have:

43m + 38m + 16m + X = 122m

Solving this for X we get:

97m + X = 122m

X = 122m - 97m = 25m

So she finally goes 25m south.

Now let's analyze how her position changes:

First, she starts at 0m

Then she goes north for 43m, then her new position is:

0m + 43m = 43m

Now she goes 38m south, then her new position is:

43m - 38m = 5m

Then she goes north again, for 16m

Then the new position is:

5m + 16m = 21m

Now she goes south for 25m, then the final position is:

21m - 25m = -4m

The displacement is equal to the difference between the final position and the initial one, so the displacement is:

-4m - 0m = -4m

The displacement is -4m.