While following the directions on a treasure

map, a pirate walks 24.3 m north, then turns
and walks 4.3 m east.
What is the magnitude of the single
straight-line displacement that the pirate
could have taken to reach the treasure?
Answer in units of m

D = sqrt((24.3)^2+(4.3)^2) = 24.7m.

24.7

To find the magnitude of the single straight-line displacement, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length 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, the northern distance and eastern distance form the two sides of a right-angled triangle, with the straight-line displacement being the hypotenuse.

Using the given values:
Northern distance = 24.3 m
Eastern distance = 4.3 m

To find the straight-line displacement, we can apply the Pythagorean theorem:

Straight-line displacement^2 = (Northern distance)^2 + (Eastern distance)^2

Substituting the given values:
Straight-line displacement^2 = (24.3 m)^2 + (4.3 m)^2

Calculating:
Straight-line displacement^2 = 591.49 m^2 + 18.49 m^2
Straight-line displacement^2 = 609.98 m^2

To find the magnitude of the straight-line displacement, we take the square root of both sides:

Straight-line displacement = √(609.98 m^2)
Straight-line displacement ≈ 24.7 m

Therefore, the magnitude of the single straight-line displacement that the pirate could have taken to reach the treasure is approximately 24.7 m.