Calculating Velocity and Time with Wind: A Homework Problem

[iam911]

Homework Statement

An airplane flies 142 mi/hr with respect to the air. On this day, the air is moving at 52 mi/hr due north with respect to the ground. What would be the velocity of the plane with respect to the ground,vpg, if the plane were pointed in each of the following directions?
How long would it take the plane to cross a state whose eastern and western borders are parallel lines 320 mi apart if the nose of the plane were pointed 45 degrees east of north? The wind is still blowing.

Homework Equations

trig functions. Pythagorean thereom

The Attempt at a Solution

Okay, so I have tried doing the problem where when I do 45 degrees east of north, my velocity for the plane is 182.3 mi/h, and then I divide 320 by 182.3 and I get around 1.76, but that is not the correct answer why? Any help would be appreciated.

 

[zgozvrm]

First of all, your question is incomplete; In the first part of the question, we are asked what the velocity of the plane is, with respect to the ground, "in each of the following directions." --- WHAT following directions?

For the second part of the question (crossing the state), break the plane's speed into it's x- and y-components. How does the wind affect these values?

 

[iam911]

The first parts, I had already answered, sorry forgot to delete it from the post, and when I break it I get 100.8 for the x-component and 152 for the y-component, and the hypotenuse is 182.3, but I still can't get the answer unless I'm doing something wrong.

 

[zgozvrm]

Your values are slightly off ... show us your work so that we can see how you got them.

You have two vectors: the plane's and the wind's. The wind affects the planes heading. Break both vectors into their x- and y- components (the wind's is easy). Add the respective components together. The result is the x- and y- component of the resultant vector (the actual path taken by the plane).

Remember that the time it takes for the plane to travel directly to a specific destination is dependent only on the component of the plane's resultant vector having the same direction as the destination (in relation to the plane's starting point).

 

[AC130Nav]

Homework Statement

An airplane flies 142 mi/hr with respect to the air. On this day, the air is moving at 52 mi/hr due north with respect to the ground. What would be the velocity of the plane with respect to the ground,vpg, if the plane were pointed in each of the following directions?
How long would it take the plane to cross a state whose eastern and western borders are parallel lines 320 mi apart if the nose of the plane were pointed 45 degrees east of north? The wind is still blowing.

Homework Equations

trig functions. Pythagorean thereom

The Attempt at a Solution

Okay, so I have tried doing the problem where when I do 45 degrees east of north, my velocity for the plane is 182.3 mi/h, and then I divide 320 by 182.3 and I get around 1.76, but that is not the correct answer why? Any help would be appreciated.

I got 182.5 mph, but that's not your problem. Do these borders 320 mi apart run north/south? If so, you are not crossing them at your velocity along track. What was the x component of your wind triangle plot?