A swimmer travels in a northerly direction across a 500 m wide lake. Once across, the swimmer notices that she is 150 m east of her original starting position. Determine the distance traveled and displacement.
draw the right triangle
distance swum: 500, right?
but the distance traveled is the same as the displacement, right?
displacement: d^2 = 500^2 + 150^2
To solve this problem, we can use the Pythagorean theorem to calculate the distance traveled and displacement.
Step 1: Distance Traveled
The distance traveled is the total path length that the swimmer covered. In this case, the swimmer traveled in a straight line across the width of the lake, which is 500 meters. Additionally, the swimmer traveled 150 meters east after crossing the lake.
To calculate the total distance traveled, we can use the Pythagorean theorem. Let's assume the distance traveled is "d."
Using the Pythagorean theorem:
d^2 = 500^2 + 150^2
We can now solve for "d" using this equation:
d = √(500^2 + 150^2)
Calculating this, we find that the swimmer traveled approximately 518.19 meters.
Therefore, the distance traveled by the swimmer is approximately 518.19 meters.
Step 2: Displacement
The displacement represents the straight-line distance and direction from the starting point to the final position of the swimmer. In this case, the swimmer is 150 meters east of her original starting position, and the lake is 500 meters wide in the north-south direction.
To calculate the displacement, we can again use the Pythagorean theorem. Let's assume the displacement is "d_displacement."
Using the Pythagorean theorem:
d_displacement^2 = 500^2 + 150^2
We can now solve for "d_displacement" using this equation:
d_displacement = √(500^2 + 150^2)
Calculating this, we find that the displacement is approximately 530.33 meters.
Therefore, the displacement of the swimmer is approximately 530.33 meters.