How Does Wind Affect the Flight Time of a Plane on a Square Route?

In summary, the total time for the plane to complete the journey is 280 seconds. This is calculated by dividing the total distance traveled (6 km) by the relative velocity of the plane (82.46 km/h). However, the assumption that the relative velocity is the same in all directions is incorrect. Each side of the square must be considered separately, taking into account the direction of the wind and the resulting changes in the plane's relative velocity.
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Homework Statement


A plane flies a square route with each side 1500m in length (north, west, south then east) If a wind was blowing from the east at 20 km/h the entire trip, find the total time it will take for the plane to complete the journey, given that the plane is flying at 80 km/h


Homework Equations


t = d/v
vog = vom + vmg? (except this is in the air)


The Attempt at a Solution


since its a square, i figure the relative velocity of all directions will be the same.
i used pythagorean theorem to find the velocity of the plane when it is affected by the wind. i got 82.46 km/h. then i used the formula t = d/v.
i used 1500m x 4 (because there are 4 routes in the square). converted this to 6 km.
then divided it by the relative velocity (82.46 km/h)
this worked out to be around 262 seconds.
the answer is supposed to be 280 seconds.

what did i do wrong?
 
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  • #2
since its a square, i figure the relative velocity of all directions will be the same.
No, this is not a correct assumption. Think about what happens when the plane flies west (in the same direction as the wind). What will be the relative velocity in that case? What about when the plane is flying eastwards (into the wind)? How do the velocities add up then?

You must consider each side of the square separately.
 
  • #3



It seems like you have made a small mistake in your calculation. The total distance traveled by the plane is not 6 km, but rather 6 km + 20 km (due to the wind). Therefore, the correct distance to use in the equation t = d/v would be 6 km + 20 km = 26 km. This would give a total time of approximately 280 seconds, as expected. It is important to be careful with units and to double check your calculations to avoid errors. Overall, your approach and use of the correct equations were correct.
 

1. What is motion in two dimensions?

Motion in two dimensions refers to the movement of an object along both the x and y axes. This means that the object is moving in both a horizontal and vertical direction simultaneously.

2. How is motion in two dimensions different from motion in one dimension?

Motion in one dimension only involves movement along a single axis, while motion in two dimensions involves movement along both the x and y axes. This means that the object is traveling in a curved path rather than a straight line.

3. What are the equations used to calculate motion in two dimensions?

The equations used to calculate motion in two dimensions are the same as those used in one-dimensional motion, but they are applied separately to the x and y components of the motion. These equations include distance, velocity, and acceleration formulas.

4. How is velocity calculated in two dimensions?

In order to calculate velocity in two dimensions, we use the Pythagorean theorem to find the resultant velocity, which is the combination of the x and y components of the motion. The x and y components can be found by multiplying the overall velocity by the cosine and sine of the angle of motion, respectively.

5. What factors can affect motion in two dimensions?

There are several factors that can affect motion in two dimensions, including velocity, acceleration, and the angle of motion. Other external forces such as friction or air resistance can also have an impact on the object's motion in two dimensions.

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