Maths or physics Interception question

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In summary, aircraft 1 and aircraft 2 will pass each other at a distance of 100 nm from airport A. Both aircraft leave at the same time, with aircraft 1 traveling at 100kts and aircraft 2 traveling at 200kts. This can be solved by setting up an equation and solving for the time they pass each other, which can then be used to determine the distance aircraft 1 travels. Alternatively, understanding the proportional relationship between speed and distance allows for a quick solution by setting up a simple equation and solving for the distance traveled by aircraft 1.
  • #1
High_flier
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Two airports (A and B) are 200nm apart. Aircraft 1 leaves airport A and
flies to B at 100kts. Aircraft 2 leaves airport B and flies to A at 200kts.
Both aircraft leave at the same time, where relative to airport A will they
pass each other?

nm=nautical miles
kts=kts
 
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  • #2
Here's one way to solve this. Call the time at which they pass each other t. During that time, each flies a certain distance D = V t. So aircraft 1 travels a distance [itex]D_1 = V_1 t[/itex] and aircraft 2 travels a distance [itex]D_2 = V_2 t[/itex]. But the total distance traveled by both aircraft must equal the distance between A and B (200 nm). I'll leave the next step to you: set up the equation and solve for t, then plug t into solve for [itex]D_1[/itex].

Once you understand what's happening, you can practically do this problem in your head. Realize that the distance each aircraft travels is proportional to its speed. Aircraft 1 travels half as fast as aircraft 2, so it travels half the distance of aircraft 2. If aircraft 1 travels D, aircraft 2 travels 2D. The total is 3D = 200 nm. Solve for D.
 
  • #3


In order to solve this interception question, we need to use the formula: Distance = Rate x Time.
First, let's convert the speeds to nautical miles per hour (nmph) since the distance is given in nautical miles.
100 kts = 115.08 nmph
200 kts = 230.15 nmph

Next, we can set up a table to represent the distance each aircraft covers in a certain amount of time:

| Aircraft | Rate (nmph) | Time (hours) | Distance (nm) |
|----------|-------------|--------------|---------------|
| 1 | 115.08 | x | 115.08x |
| 2 | 230.15 | x | 230.15x |

Since both aircrafts leave at the same time, we can set the times equal to each other:
115.08x = 230.15x
Solving for x, we get x = 2.
This means that after 2 hours, both aircrafts will have traveled a certain distance and will pass each other.
To find out where they will pass each other relative to airport A, we can plug in x = 2 into the distance formula:
Aircraft 1: 115.08 x 2 = 230.16 nm
Aircraft 2: 230.15 x 2 = 460.3 nm
Therefore, they will pass each other 230.16 nm from airport A.
In conclusion, after 2 hours, both aircrafts will pass each other 230.16 nm from airport A.
 

1. What is the difference between maths and physics?

Mathematics is a branch of science that deals with numbers, quantities, shapes, and patterns. It involves using logic and abstract concepts to solve problems. Physics, on the other hand, is a branch of science that studies the fundamental laws of nature and how the universe works. It involves using mathematical equations and experiments to understand and explain physical phenomena.

2. How are maths and physics related?

Mathematics and physics are closely related, as mathematics provides the language and tools for understanding and describing physical laws and phenomena. Many concepts and theories in physics are built upon mathematical principles, and mathematical equations are used to make predictions and test hypotheses in physics.

3. What is an interception question in maths or physics?

An interception question in maths or physics is a type of problem that involves finding the point at which two lines or objects intersect. This can be in the form of finding the coordinates of the intersection point or the time at which two moving objects will meet. It requires knowledge of algebra, geometry, and/or calculus to solve.

4. How do you approach an interception question in maths or physics?

To solve an interception question, you first need to identify the two lines or objects involved and determine what information is given. Then, use the appropriate mathematical formulas or equations to find the coordinates or time of intersection. It is important to clearly define your variables and show all steps of your solution to ensure accuracy.

5. Why are interception questions important in maths and physics?

Interception questions are important in maths and physics because they allow us to solve real-world problems and make predictions about the behavior of objects in motion. They also help us understand the relationship between different variables and how they affect each other. Interception questions can be found in many areas of science and engineering, making them a valuable skill to have for any scientist or mathematician.

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