an airplane flies 800 km east and 600 in north. What is the total displacement (with approximate direction)? What is the total distance traveled?
Draw a diagram to find displacement.
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800km east
Something like that haha (it's not drawn to scale.) Close up the triangle and the hypotenuse is the displacement. Use pythagoras' theorem to compute.
For distance, since direction is not taken into account as it is a scalar quantity, you can add up the total distance covered. i.e. 600+800km
To find the total displacement, we can use the Pythagorean theorem to calculate the magnitude of the displacement and trigonometry to determine the direction.
Step 1: Calculate the magnitude of the displacement.
Let's consider the displacement along the East direction as the x-component (800 km) and displacement along the North direction as the y-component (600 km). According to the Pythagorean theorem, the magnitude of the displacement (d) can be calculated as:
d = √(x² + y²)
d = √((800 km)² + (600 km)²)
d = √(640,000 km² + 360,000 km²)
d = √(1,000,000 km²)
d ≈ 1000 km
Therefore, the magnitude of the displacement is approximately 1000 km.
Step 2: Determine the direction of the displacement.
To find the direction, we can use the tangent function:
tan θ = y / x
θ = tan^(-1)(y / x)
θ = tan^(-1)(600 km / 800 km)
θ = tan^(-1)(0.75)
θ ≈ 36.87°
Therefore, the direction of the displacement is approximately 36.87° north of east.
Now, let's calculate the total distance traveled.
The distance traveled is the sum of the magnitudes of the displacements in each direction.
Total distance = 800 km + 600 km
Total distance = 1400 km
Thus, the total distance traveled is 1400 km.
To summarize:
- The total displacement is approximately 1000 km at approximately 36.87° north of east.
- The total distance traveled is 1400 km.