Introductory Vector Problem- Airplane emergency landing

In summary, a plane flying from Galisteo changes direction and makes an emergency landing after traveling 180 km at 67.0 degrees east of north and 255 km at 49.0 degrees south of east. When a rescue crew is sent from the airport, they should fly approximately 310 km directly to the plane. This calculation is based on the distance between the two points, which is at least 333 km.
  • #1
Jarvis88
14
0

Homework Statement


[/B]
A plane leaves the airport in Galisteo and flies 180 km at 67.0 degrees east of north; then it changes direction to fly 255 km at 49.0 degrees south of east, after which it makes an immediate emergency landing in a pasture.

When the airport sends out a rescue crew, how far should this crew fly to go directly to this plane

The Attempt at a Solution


I assume I need the angle as measured counterclockwise from the x-axis,
90deg - 67deg =23deg

Ax = 180cos23 =165.69 km
Ay = 180sin23 =70.33 km

Bx = 255cos49 =167.295 km
By = -255sin49 = -192.45 (because I have my vector pointed in the negative y direction along the positive x-axis)

Ax+Bx = 332.99 km
Ay+By = -122.12 km

R= sqrt [(332.99^2)+(122.12^2)]
R= 310 km

I'm not sure where I've gone wrong. I also used Ax=180sin67 and Ay=180cos67, which give the same numbers (because they're complimentary angles?). I didn't round my numbers when I calculated everything; I put in the exact numbers when I added and took the square root.
Mastering Physics says I'm wrong, but doesn't provide a hint as to why.
 
Physics news on Phys.org
  • #2
Jarvis88 said:
R= sqrt [(332.99^2)+(122.12^2)]
This number must be at least 333 ...
 
  • Like
Likes Jarvis88
  • #3
Orodruin said:
This number must be at least 333 ...

Thank you! I rechecked my math, and somehow I must not have entered it into my calculator correctly. This may be a silly question, but how would I know it's supposed to be at least 333? Is it because 333 was the largest squared number and it was added to the other number?
 

FAQ: Introductory Vector Problem- Airplane emergency landing

1. What is an introductory vector problem?

An introductory vector problem is a type of mathematical problem that involves using vectors, which are mathematical quantities that have both magnitude and direction, to solve real-world scenarios.

2. What is an "airplane emergency landing" vector problem?

An "airplane emergency landing" vector problem is a specific type of introductory vector problem that involves using vectors to model and solve a scenario where an airplane needs to make an emergency landing.

3. What are the main components of an "airplane emergency landing" vector problem?

The main components of an "airplane emergency landing" vector problem are the initial position of the airplane, its velocity, and the direction and magnitude of any external forces acting on the airplane (such as wind or engine failure).

4. How are vectors used to solve an "airplane emergency landing" problem?

Vectors are used to represent the various physical quantities involved in an "airplane emergency landing" problem, such as the airplane's position, velocity, and forces acting on it. By using vector addition and subtraction, these quantities can be combined and manipulated to find the optimal solution for the emergency landing.

5. What are some real-world applications of solving "airplane emergency landing" vector problems?

Solving "airplane emergency landing" vector problems can have practical applications in the fields of aeronautics, aviation safety, and emergency preparedness. By understanding how vectors can be used to model and solve emergency scenarios, engineers and pilots can better prepare for and respond to potential emergencies in the real world.

Back
Top