How to Calculate Time and Distance for a Plane Flying with Wind and Vectors

In summary, the problem involves a plane flying north a distance of 283 km to the west, with a wind blowing north at 56 km/h. The plane's speed is 843 km/h. The question is asking for the time needed to reach the western position, the distance north or south from the original position, the actual distance the plane flew, and the actual speed of the plane. The only known equation is the Pythagorean theorem, a2+b2=c2. One attempt at a solution involved using speed=distance/time to find the time needed to reach the western position, but there is uncertainty about how to approach the rest of the problem.
  • #1
cwalden91
3
0

Homework Statement


"A plane flies north a distance of 283 km to the west. There is a wind blowing to the north at 56km/h. The plane's speed is 843 km/h. How much time is needed to get to the western position? How far north or south will the plane be from the original position? What is the actual distance the plane flew? What is the actual speed of the plane?"


Homework Equations


The only equation given to us thus far relating to vectors is the Pythagorean theorem : a2+b2=c2


The Attempt at a Solution


The only part of this question I was able to answer was the first part about the time. I used speed=distance/time to get time=0.336 hours. I don't even know where to start for the rest of this problem. I'm desperately in need of help.
 
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  • #2
A plane flies north a distance of 283 km to the west.

I think whoever wrote this question has a variant of English unknown to most of us.
 
  • #3
Well it was my Physics teacher...and he's quite American so...I don't know why he wrote it oddly.
 

Related to How to Calculate Time and Distance for a Plane Flying with Wind and Vectors

1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. In a plane problem, a vector is often represented as an arrow with a specific length and direction.

2. How do you add two vectors?

To add two vectors in a plane problem, you can use the parallelogram law. This involves drawing the two vectors as sides of a parallelogram and finding the diagonal, which represents the resultant vector.

3. How do you find the magnitude of a vector?

The magnitude of a vector is its length. In a plane problem, you can find the magnitude of a vector by using the Pythagorean theorem, which involves finding the square root of the sum of the squares of its components.

4. What is the difference between a scalar and a vector?

A scalar is a mathematical quantity that only has magnitude, while a vector has both magnitude and direction. For example, speed is a scalar quantity, while velocity (speed with direction) is a vector quantity.

5. How do you resolve a vector into its components?

To resolve a vector into its components, you can use trigonometry. The magnitude of the horizontal component can be found by multiplying the magnitude of the vector by the cosine of the angle it makes with the horizontal axis. Similarly, the magnitude of the vertical component can be found by multiplying the magnitude of the vector by the sine of the angle it makes with the horizontal axis.

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