[Math] Finding Ground Speed

vectors

I have trouble with homework question i can't seem to figure out. I have tried have method below to solving. I am not sure am i correct because my answer is wrong.

A jet is heading due east: its nose points towards the east direction, but its trajectory on the ground deviates from the east direction due to a sideways component of the wind. The plane is also climbing at the rate of 100 km/h (height increase per unit time). If the plane's airspeed is 510 km/h and there is a wind blowing 90 km/h to the northwest, what is the ground speed of the plane?

$$c^2=510^2-90+2\cdot \sqrt{510-100}\cdot \cos 45°$$

Best Answer

HINT

Let indicate

  • $\vec X=x\, \vec i\quad$ the unknown horizontal ground speed
  • $\vec Y=y\, \vec j=90\, \vec j\quad$ the drag horizontal NE wind speed
  • $\vec Z=z\,\vec k=100\,\vec k\quad $ the climbing vertical speed

and we know that

$$\sqrt{x^2+y^2+z^2}=510$$

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