Plane direction and veloctiy question

[mathzing]

alright, here is the question and how far i got.

A light plane is traveling at 175km/h on a heading of N8[degree]E in a 40km/h wind from N80[degrees]East. Determine the planes ground velocity

im going to skip the notations so..

planes velocity relative to the air is (175cos8, 175sin8)
= (173.2,24.3)

air velocity relative to the ground is (40cos80, 40sin80)
= (6.94,39.4)

you add both and get (180.14,63.7)

and the magnitude which is the velocity of the plance relative to the air is 191.07km/h

191.07km/h is wrong, it should be 167 km/h.

I don't understand what i am doing wrong.
Yes, i do know how to find the direction, but if the speed is wrong there is no point in trying to find the direction becuase it too would be wrong. any ideas on how to fix?

 

[radou]

Draw your vectors, it will be more easy to determine what you're doing wrong.

 

[kyle8921]

As a scientist, it is important to always double check your calculations and equations to ensure accuracy. In this case, it seems like there may have been a mistake in the way the air velocity was calculated. The correct values for the air velocity relative to the ground should be (40cos10, 40sin10) = (38.7,6.94). When you add this to the plane's velocity relative to the air, you should get a ground velocity of (212.0,31.2) which has a magnitude of approximately 215 km/h. This is closer to the expected value of 167 km/h, but it is still slightly off. It is possible that there may be other factors at play, such as air resistance or changes in wind speed and direction. It would be helpful to double check the given information and equations, and also consider any other factors that may affect the plane's ground velocity.