Determine the plane's ground velocity.

In summary, the problem involves a light plane traveling at 175km/h on a heading of 8° east of north in a 40-km/h wind from 80° east of north. The resultant ground velocity is calculated using the cosine law and is found to be 191 km/h. However, the correct answer is 167 km/h due to error in drawing the triangle and incorrect addition of vectors. The correct approach is to subtract the two vectors, P and G, to find the difference P - G, which is equal to (P - A) + (A - G).
  • #1
a.a
127
0

Homework Statement



1 A light plane is traveling at 175km/h on a heading of 8° east of north in a 40-km/h wind from 80° east of north. Determine the plane's ground velocity.

Homework Equations



cosine law


The Attempt at a Solution


I found the resultant to be 191 km/h but the answer is 167 km/h
 
Last edited:
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  • #2
Show us your working a.a it will help us see where you have gone wrong if you have. :smile:
 
  • #3
a.a said:
I found the resultant to be 191 km/h but the answer is 167 km/h

Hi a.a! :smile:

You've added the 2*40*175*cos72 instead of subtracting it.

I expect you've drawn the triangle wrong.

If the velocity of the plane the air and the ground are P A and G, then the question asks for P - G, which is (P - A) + (A - G).

Draw the triangle so that the arrows go the right way. :smile:
 

1. What is ground velocity?

Ground velocity refers to the speed and direction of an object relative to the ground. In the case of a plane, it is the speed and direction at which the plane is moving over the Earth's surface.

2. How is ground velocity different from airspeed?

Airspeed is the speed of an object relative to the air, while ground velocity takes into account the movement of the air itself. This means that ground velocity may be affected by factors such as wind speed and direction, while airspeed is not.

3. How is ground velocity measured?

Ground velocity can be measured using instruments such as GPS (Global Positioning System) or by using mathematical calculations based on the plane's airspeed, heading, and wind speed.

4. Why is it important to determine the plane's ground velocity?

Knowing the plane's ground velocity is important for navigation and flight planning. It allows pilots to accurately determine their position, track their progress, and adjust their flight path if needed.

5. Can ground velocity change during a flight?

Yes, ground velocity can change during a flight due to factors such as wind speed and direction. Pilots must constantly monitor and adjust for these changes to ensure a safe and efficient flight.

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