While following the directions on a treasure
map, a pirate walks 37.8 m north, then turns
and walks 5.2 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.
Y = 37.8 m.
X = 5.2 m.
Disp. = Sqrt(X^2 + Y^2) =
To find the magnitude of the single straight-line displacement, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the pirate has walked 37.8 m north and 5.2 m east. This forms a right triangle, where the northward distance is the vertical leg and the eastward distance is the horizontal leg. The single straight-line displacement is the hypotenuse.
We can use the formula:
c^2 = a^2 + b^2
where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
In this case, a = 37.8 m (northward distance) and b = 5.2 m (eastward distance).
Plugging these values into the formula, we have:
c^2 = (37.8)^2 + (5.2)^2
c^2 = 1428.84 + 27.04
c^2 = 1455.88
To find c, we take the square root of both sides:
c ≈ √1455.88
c ≈ 38.16 m
Therefore, the magnitude of the single straight-line displacement that the pirate could have taken to reach the treasure is approximately 38.16 meters.