While following the directions on a treasure map, a pirate walks 23.5 m north, then turns and walks 2.7 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
Here's what you know,
Dy = 23.5 m, and Dx = 2.7m.
Use the formula
d = (Dx^2 + Dy^2)^ (1/2)
d = (23.5^2 + 2.7^2)^((1/2) = 23.65m
d = 24m (significant digits).
Since they have only asked for magnitude, its 24m.
If they ask for direction then,
theta = tan-1( Dy / Dx )
= tan-1( 23.5 / 2.7)
theta = 83.4 deg or 83 deg (significant digits)
To find the magnitude of the single straight-line 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 northward displacement (23.5 m) is one side of the right triangle, and the eastward displacement (2.7 m) is the other side. The displacement we want to find is the hypotenuse.
To calculate the magnitude of the displacement, we can use the formula:
displacement = √(northward^2 + eastward^2)
Substituting the values:
displacement = √(23.5^2 + 2.7^2)
displacement = √(552.25 + 7.29)
displacement = √(559.54)
displacement ≈ 23.67 m
Therefore, the magnitude of the single straight-line displacement that the pirate could have taken to reach the treasure is approximately 23.67 m.