two ships leave the same port at the same time. One travels north at 12 miles per hour. The other travel west at 5 miles per hour. After four hours, how far apart are the two ships?
4 * 12 = 48
4 * 5 = 20
Pythagorean Theorem:
48^2 + 20^2 = c^2
To find the distance between the two ships after four hours, we can use the Pythagorean theorem since they are moving perpendicular to each other.
First, let's find the distance the northbound ship has traveled. The formula to calculate distance is speed multiplied by time.
Distance = Speed * Time
Distance = 12 miles/hour * 4 hours
Distance = 48 miles
Next, let's find the distance the westbound ship has traveled.
Distance = Speed * Time
Distance = 5 miles/hour * 4 hours
Distance = 20 miles
Using the Pythagorean theorem, we can calculate the distance between the two ships.
Distance² = (48 miles)² + (20 miles)²
Distance² = 2304 miles² + 400 miles²
Distance² = 2704 miles²
Distance ≈ √2704 miles
Distance ≈ 52 miles
Therefore, after four hours, the two ships are approximately 52 miles apart.
To find the distance between the two ships after four hours, we can use the Pythagorean theorem. Let's break down the problem step by step:
1. Determine the distance traveled by each ship after four hours:
- The ship traveling north has been moving at a speed of 12 miles per hour for four hours. So, the distance traveled by this ship is 12 miles/hour * 4 hours = 48 miles.
- The ship traveling west has been moving at a speed of 5 miles per hour for four hours. So, the distance traveled by this ship is 5 miles/hour * 4 hours = 20 miles.
2. Visualize the position of the ships on a coordinate plane:
- Place the starting point (port) as the origin (0,0).
- The ship traveling north will be at the point (0, 48), since it hasn't moved horizontally but has moved 48 miles vertically.
- The ship traveling west will be at the point (-20, 0), since it hasn't moved vertically but has moved 20 miles horizontally.
3. Calculate the distance between the two ships using the Pythagorean theorem. The formula is:
- Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates.
- For our case, the coordinates are: (0, 48) and (-20, 0).
- Distance = sqrt((-20 - 0)^2 + (0 - 48)^2) = sqrt((-20)^2 + (-48)^2) = sqrt(400 + 2304) = sqrt(2704) = 52 miles (approximately).
After four hours, the two ships will be approximately 52 miles apart.