A car travels 20 km southwards and then another 30 westwards. What is the displacement of the car from its initial position?
use the Pythagorean Theorem, since the directions are perpendicular.
10km
To find the displacement of the car from its initial position, we need to use the Pythagorean theorem. The displacement is the straight-line distance between the initial and final positions of the car.
First, let's draw a diagram to visualize the car's movement. Take a point as the initial position and mark it as the origin (0, 0).
Starting from the origin, the car travels 20 km southwards. This means that the car moves downwards from the origin by 20 km. So, mark the position after traveling 20 km below the origin as point A.
Next, the car travels 30 km westwards from point A. This means that the car moves towards the left (west) from point A by 30 km. Mark this position as point B.
We now have two sides of a right-angled triangle - one side with a length of 20 km (vertical) and the other side with a length of 30 km (horizontal). The displacement will be the hypotenuse of this triangle, which we can find by applying the Pythagorean theorem.
Using the formula a^2 + b^2 = c^2, where a and b are the lengths of the two sides, and c is the length of the hypotenuse, we can calculate the displacement as follows:
20^2 + 30^2 = c^2
400 + 900 = c^2
1300 = c^2
To find the value of c, we need to take the square root of both sides:
√1300 = √c^2
36.055 = c
Therefore, the displacement of the car from its initial position is approximately 36.055 km.