While following the directions on a treasure map, a pirate walks 37.0 m north and then turns and walks 8.5 m east. What is the magnitude of his resultant displacement?
A: 38 m
B: 45.5 m
C: 28.5 m
4. What is the direction (including angle) of the pirate’s displacement in question #3?
A: 13 degrees north of east
B: 77 degrees north of east
C: 13 degrees north
D: 77 degrees north
3. d^2 = 37.0^2 + 8.5^2
4. Θ is the angle measured from the x-axis ... tan(Θ) = 37.0 / 8.5
To find the magnitude of the resultant displacement, we can use the Pythagorean theorem. The Pythagorean theorem 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, the pirate walked 37.0 m north and then 8.5 m east, forming a right triangle. The north and east displacements are the two sides of the triangle.
To find the magnitude of the resultant displacement, we need to find the length of the hypotenuse, which represents the total displacement.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
Hypotenuse^2 = North Displacement^2 + East Displacement^2
Hypotenuse^2 = (37.0 m)^2 + (8.5 m)^2
Hypotenuse^2 = 1369 m^2 + 72.25 m^2
Hypotenuse^2 = 1441.25 m^2
To find the magnitude of the resultant displacement, we need to take the square root of both sides:
Hypotenuse = √1441.25 m^2
Hypotenuse ≈ 37.97 m
Rounding to the nearest meter, the magnitude of the pirate's resultant displacement is approximately 38 m.
Therefore, the correct answer is A: 38 m.
√(37.0^2 + 8.5^2) = ______
the angle x (north of east) is such that
tan(x) = 37/8.5