What Is the Ground Speed of a Plane with a North Wind?

In summary, the problem involves determining the speed of a plane with respect to the ground based on the compass reading and air speed indicator. The attempt at a solution involved setting up a right triangle and using the equation c = √(c_x^2 + c_y^2), but the online submission was broken and only accepted an answer of 219 km/hr instead of the correct answer of 220 km/hr.
  • #1
Euler2718
90
3

Homework Statement



The compass in a plane indicates that the plane is pointed due east; its air speed indicator reads 212 km/hr. There is a steady wind blowing from the north with a speed of 60.0 km/hr. What is the speed of the plane with respect to the ground?

Homework Equations



[tex] \sqrt{c^{2}_{x} + c^{2}_{y} } = |c| [/tex]

I think

The Attempt at a Solution


[/B]
I tried setting up a right triangle but nothing works. Can someone point me in the right direction, I'm very frustrated.
 
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  • #2
What are you using for c_x and c_y in your equation? That appears to be the right way to approach this problem.
 
  • #3
RUber said:
What are you using for c_x and c_y in your equation? That appears to be the right way to approach this problem.
Yeah the online submission was broken. The answer was 220 km/hr, but it would only take 219 km/hr as the answer. All good now.
 
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FAQ: What Is the Ground Speed of a Plane with a North Wind?

What is the definition of "Plane Speed Relative to Ground"?

Plane Speed Relative to Ground is the speed of an aircraft in relation to the surface of the earth. It takes into account the motion of the plane in the air as well as the rotation of the earth.

How is "Plane Speed Relative to Ground" different from "Air Speed"?

Plane Speed Relative to Ground and Air Speed are different measurements. Air Speed only takes into account the motion of the plane through the air, while Plane Speed Relative to Ground also considers the movement of the earth below the plane.

What factors affect "Plane Speed Relative to Ground"?

Several factors can affect Plane Speed Relative to Ground, including wind speed and direction, the altitude of the plane, and the rotation of the earth. The speed and direction of the wind can either increase or decrease the plane's speed relative to the ground, while changes in altitude can also affect the plane's speed.

How is "Plane Speed Relative to Ground" measured?

"Plane Speed Relative to Ground" is typically measured using an instrument called an airspeed indicator. This instrument takes into account the plane's airspeed and adjusts it based on the effects of wind and altitude to calculate the plane's speed relative to the ground.

Can "Plane Speed Relative to Ground" ever be faster than the plane's Air Speed?

Yes, it is possible for Plane Speed Relative to Ground to be faster than the plane's Air Speed. This can occur when the plane is flying with a tailwind, meaning the wind is blowing in the same direction as the plane's flight path. In this case, the plane's speed relative to the ground will be the sum of the airspeed and the wind speed, resulting in a faster overall speed relative to the ground.

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