While following the directions on a treasure
map, a pirate walks 25.2 m north, then turns
and walks 4.4 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.
25.58 m
4.4^2 x 25.2^2 = x^2
sqrt(x) = 25.58
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. The theorem states that in a right 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 pirate has traveled 25.2 m north and 4.4 m east. These two sides of the triangle are perpendicular to each other, making a right-angled triangle. We can use the Pythagorean theorem to find the length of the hypotenuse, which represents the single straight-line displacement.
Let's calculate it step by step:
Step 1: Square the length traveled north:
(25.2 m)² = 634.56 m²
Step 2: Square the length traveled east:
(4.4 m)² = 19.36 m²
Step 3: Add the squares of the two sides:
634.56 m² + 19.36 m² = 653.92 m²
Step 4: Take the square root of the sum to find the magnitude of the single straight-line displacement:
√(653.92 m²) ≈ 25.6 m
Therefore, the magnitude of the single straight-line displacement the pirate could have taken to reach the treasure is approximately 25.6 meters.