A ship at sea is due into a port 600 km due south in two days. However, a severe storm comes in and blows it 200 km due east from its original position. How far is the ship from its destination?
X = 200 km.
Y = -600 km.
d^2=X^2 + Y^2=200^2 + (-600)^2=400,000
d = 632 km.
d^2 = 600^2 + 200^2
To find the distance of the ship from its destination, we can use the Pythagorean theorem. Let's break down the given information step-by-step:
1. The ship is due south of its destination, 600 km away.
2. The storm blows the ship 200 km due east from its original position.
To visualize this, we can draw a right-angled triangle with the ship's original position, its new position, and its destination:
|\
| \
| \ 600 km
| \
| \
-------
We can calculate the distance of the ship from its destination by finding the hypotenuse of this right-angled triangle.
Using the Pythagorean theorem:
c² = a² + b²
Where:
c is the hypotenuse (distance from the ship's new position to the destination)
a is the side length of the triangle opposite to the destination (600 km)
b is the side length of the triangle adjacent to the destination (200 km)
Let's substitute the given values into the equation:
c² = (600 km)² + (200 km)²
c² = 360,000 km² + 40,000 km²
c² = 400,000 km²
To find c, we take the square root of both sides of the equation:
c = √400,000 km²
c ≈ 632.46 km
Therefore, the ship is approximately 632.46 km from its destination.
To find the distance between the ship's current position and its destination, we can use the Pythagorean theorem. This theorem states that in a right-angled 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 ship's current position, due to the storm, can be represented as a right-angled triangle with one side measuring 200 km (east) and the other side measuring 600 km (south).
First, let's calculate the distance the ship traveled south by subtracting the ship's initial position from its destination: 600 km - 0 km = 600 km.
Now, let's calculate the distance between the ship's current position and its destination using the Pythagorean theorem:
Distance² = (Distance traveled south)² + (Distance traveled east)²
Distance² = (600 km)² + (200 km)²
Distance² = 360,000 km² + 40,000 km²
Distance² = 400,000 km²
Taking the square root of both sides, we find:
Distance = √400,000 km²
Distance ≈ 632.45 km
Therefore, the ship is approximately 632.45 km away from its destination.