An aircraft flies 800km due east and the 600km due north.Determine the magnitude of it's displacement
Disp. = 800 + 600i
Disp. = sqrt(X^2+Y^2) = sqrt(800^2+600^2) =
To determine the magnitude of the displacement of an aircraft that flies 800km due east and then 600km due north, we can use the Pythagorean theorem.
The Pythagorean 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 distance flown east (800km) and the distance flown north (600km) form the sides of a right-angled triangle.
Using the Pythagorean theorem, we can calculate the magnitude of the displacement:
Magnitude of displacement = √(800^2 + 600^2)
Magnitude of displacement = √(640,000 + 360,000)
Magnitude of displacement = √1,000,000
Magnitude of displacement = 1,000 km
Therefore, the magnitude of the displacement of the aircraft is 1,000 km.
To find the magnitude of the displacement, we can use the Pythagorean theorem.
The Pythagorean theorem states that for a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this scenario, the aircraft's displacement creates a right-angled triangle, with the distance traveled due east being one side (a) and the distance traveled due north being another side (b). The displacement is the hypotenuse (c).
Using the given information, we know that the aircraft flew 800km due east and 600km due north. So, a = 800km and b = 600km.
To find the magnitude of the displacement (c), we can use the formula:
c^2 = a^2 + b^2
Substituting the values, we get:
c^2 = (800km)^2 + (600km)^2
c^2 = 640,000km^2 + 360,000km^2
c^2 = 1,000,000km^2
Taking the square root of both sides, we find:
c = √1,000,000km^2
c ≈ 1000km
Therefore, the magnitude of the aircraft's displacement is approximately 1000km.