While following the directions on a treasure
map, a pirate walks 49.7 m north, then turns
and walks 4.1 m east.
What is the magnitude of the single
straight-line displacement that the pirate
could have taken to reach the treasure?
Use Pythagoras' Theorem
50m
To find the magnitude of the single straight-line displacement that the pirate could have taken to reach the treasure, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the pirate's northward and eastward steps as the two sides of a right triangle, and the straight-line displacement to the treasure as the hypotenuse.
The northward step is 49.7 m and the eastward step is 4.1 m. So, we can calculate the magnitude of the straight-line displacement using the Pythagorean theorem:
Magnitude of straight-line displacement = √(49.7^2 + 4.1^2)
Now, let's compute the magnitude:
Magnitude of straight-line displacement = √(2470.09 + 16.81)
Magnitude of straight-line displacement = √(2486.9)
Magnitude of straight-line displacement ≈ 49.87 m
Therefore, the magnitude of the single straight-line displacement that the pirate could have taken to reach the treasure is approximately 49.87 meters.