Solving 2D Motion Problem: A to B Flight Distance

In summary, the conversation is about a problem involving an airplane flying from airport A to B. The first flight goes 300 km east, 410 km at 25.5° west of north, and then 150 km north. The next day, a pilot flies directly from A to B in a straight line. The speaker was having trouble finding the correct answer and asked for advice. They eventually found the correct E and N components after getting thrown off by the "west of north" angle.
  • #1
Aubiefan
16
0
I'm having a bit of trouble with this problem, I thought I knew how to solve it but can't get what is listed as the correct answer in the key.

An airplane starting from airport A flies 300 km east, then 410 km at 25.5° west of north, and then 150 km north to arrive finally at airport B.
The next day, a pilot flies directly from A to B in a straight line, what is the distance of this flight?

I was able to find the correct angle, 77.89 degrees north of east, and I tried to use the Pythagorean theorem with the X and Y components to find the length of the resultant, but the website (it's a webassign.net problem for a class) keeps telling me I have the wrong answer. Any insights on what I'm doing wrong? The two answers I keep coming up with are 371.17 km and 333.94 km.

thanks for your time!
 
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  • #2
You have the wrong E and N components ...
the N component by itself is over 500 km (150 + almost 400).
Show your work!
 
  • #3
You can do this graphically. Make a drawing to scale, use a protractor also. Then you can tell where your errors lie.
 
  • #4
Thanks for your advice, I reworked it and found the correct components. I had gotten a little thrown by the "west of north" angle and made a mess of some negative signs when doing the trig.
Thanks again!
 

1. What is 2D motion and why is it important to solve problems related to it?

2D motion refers to the movement of an object in two dimensions, typically represented on a coordinate plane. It is important to solve problems related to 2D motion because many real-world scenarios involve objects moving in more than one direction, and understanding how to calculate and analyze this motion is crucial in fields such as physics, engineering, and navigation.

2. How do you calculate the distance between two points in 2D motion?

The distance between two points in 2D motion can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides. In 2D motion, the two sides represent the vertical and horizontal distances between the two points, and the hypotenuse represents the total distance traveled.

3. What are the key variables to consider when solving a 2D motion problem from point A to point B?

The key variables to consider in a 2D motion problem are the initial position (x0 and y0), initial velocity (v0), acceleration (a), time (t), and final position (x and y). These variables are used in equations such as x = x0 + v0t + 1/2at2 and y = y0 + v0t + 1/2at2 to calculate the distance and position of an object at any given time during its 2D motion.

4. How do you handle the angle of motion in a 2D problem?

The angle of motion in a 2D problem can be handled using trigonometric functions such as sine and cosine. These functions can be used to find the vertical and horizontal components of the object's motion, which can then be used in the equations for distance and position. Additionally, the angle can be used to determine the direction of the object's motion.

5. How can we apply 2D motion problem solving in real life situations?

2D motion problem solving can be applied in various real-life situations, such as calculating the distance and time it takes for an airplane to fly from one city to another, determining the trajectory of a thrown ball in a game, or analyzing the motion of a car on a curved road. It can also be used in fields such as sports, engineering, and navigation to understand and predict the movement of objects in two dimensions.

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