An Air Craft Flies 800km Due East And Then 600km Due North.Determine The Magnitude Of Its Displacement.
what is sqrt(800^2+600^2) km
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An aircraft flies 800km due east and then 600km due north. Determine the magnitude of its displacement.
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To determine the magnitude of the displacement, we need to use the Pythagorean theorem.
Step 1: Draw a diagram to visualize the given information. On the diagram, draw a line that represents the eastward distance (800 km), and a line perpendicular to it representing the northward distance (600 km).
Step 2: Using the Pythagorean theorem, we can calculate the displacement using the formula c² = a² + b², where c is the hypotenuse (displacement) and a, b are the lengths of the other two sides.
In this case, the eastward distance (800 km) represents side a, and the northward distance (600 km) represents side b.
Step 3: Substitute the given values into the formula:
c² = (800 km)² + (600 km)²
Step 4: Square the given values:
c² = 640,000 km² + 360,000 km²
Step 5: Add the squared values:
c² = 1,000,000 km²
Step 6: Take the square root of both sides of the equation to find the magnitude of the displacement:
c = √(1,000,000 km²)
Using a calculator, the square root of 1,000,000 km² is 1,000 km.
Therefore, the magnitude of the aircraft's displacement is 1,000 km.