Mr Lee start from her home,and goes 250m due south,then 200m due east,and finally 100 due south to a shopping mall.Find the distance between her home and shopping mall.
the final displacement is
350m south
200m east
the distance is thus √(350^2+200^2)
To find the distance between Mr Lee's home and the shopping mall, we can use the Pythagorean theorem.
Step 1: Draw a diagram to visualize the movements.
Starting from Mr Lee's home, we can represent his directions as follows:
- Going 250m due south
- Going 200m due east
- Going 100m due south to the shopping mall
Step 2: Determine the horizontal and vertical components of the distance traveled.
Since Mr Lee goes due south and due east, we need to identify the horizontal and vertical distances.
- 250m due south is a vertical movement, so we can consider it as moving down by 250m.
- 200m due east is a horizontal movement, so we can consider it as moving to the right by 200m.
- 100m due south is another vertical movement, so we can consider it as moving down by an additional 100m.
Step 3: Calculate the total horizontal and vertical distances.
- Total vertical distance = 250m + 100m = 350m (downward is considered positive)
- Total horizontal distance = 200m (rightward is considered positive)
Step 4: Apply the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the vertical and horizontal distances act as the sides of the right triangle, and we need to find the hypotenuse (distance between the home and the mall).
Using the formula:
Distance^2 = (Vertical distance)^2 + (Horizontal distance)^2
Substituting the values:
Distance^2 = 350^2 + 200^2
Calculating:
Distance^2 = 122,500 + 40,000
Distance^2 = 162,500
Taking the square root of both sides:
Distance ≈ √162,500
Distance ≈ 403.12m
Therefore, the distance between Mr Lee's home and the shopping mall is approximately 403.12 meters.