Determine the plane's ground velocity.

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To determine the plane's ground velocity, the problem involves a light plane traveling at 175 km/h at a heading of 8° east of north, with a wind speed of 40 km/h from 80° east of north. The initial calculation yielded a resultant velocity of 191 km/h, but the correct answer is 167 km/h. A key error identified in the calculations was the incorrect addition of components; instead, the wind's effect should be subtracted from the plane's airspeed. Properly drawing the velocity triangle and ensuring the vectors are oriented correctly is crucial for accurate results. The discussion emphasizes the importance of vector addition and the cosine law in solving the problem.
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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
 
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Show us your working a.a it will help us see where you have gone wrong if you have. :smile:
 
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:
 

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