An airplane flies 220 km due east, makes a right-angle, and then flies 400 km due north. Find the magnitude of the plane's displacement from it's starting point. Neglect the culrvature of the earth
You need to square both distances.
>220^2 + 400^2 =
From there, you take the square root of the result which gives you your magnitude of displacement.
Well, if we neglect the curvature of the earth, we might as well neglect the gravity too and turn this into a fun flying circus act!
So, let's imagine the airplane doing a daring acrobatic performance. It starts by flying 220 km due east, which is like doing a high-speed flying barrel roll. Then, it suddenly decides to show off its precision by making a right-angle turn and flies 400 km due north.
Now, to find the magnitude of the plane's displacement from its starting point, let's just imagine the plane's path as a straight line. We just need to draw a right-angled triangle and apply the Pythagorean Theorem, or should we say "Pythagorean Air-theorem"?
Using Pythagoras, we have the hypotenuse (c) squared as the sum of the squares of the two legs (a and b). In our case, a is 220 km and b is 400 km. So, c² = 220² + 400².
Calculating this big sum, we get c² = 48400 + 160000 = 208400. Taking the square root of that, we find c ≈ 456.12 km.
So, the magnitude of the plane's displacement from its starting point is around 456.12 km. And thanks to our fearless pilot, it might have even added a few extra kilometers of excitement to the journey!
To find the magnitude of the plane's displacement, we can use the Pythagorean theorem because the plane first traveled 220 km east and then 400 km north, forming a right triangle.
Step 1: Draw a diagram to visualize the scenario. Draw a straight horizontal line to represent the eastward distance of 220 km, and then from the end of this line, draw a straight vertical line to represent the northward distance of 400 km. This will form a right triangle.
400
______|
| |
220| |
|______|
Step 2: Apply the Pythagorean theorem. According to the theorem, the square of the hypotenuse (displacement) of a right triangle is equal to the sum of the squares of the other two sides. In this case, the displacement is the hypotenuse.
Let's call the displacement D. Using the Pythagorean theorem, we have:
D^2 = (220 km)^2 + (400 km)^2
Step 3: Calculate the magnitude of the displacement.
D^2 = 220^2 + 400^2
D^2 = 48,400 + 160,000
D^2 = 208,400
D ≈ √208,400
D ≈ 456.16 km
Therefore, the magnitude of the plane's displacement from its starting point is approximately 456.16 km.