Aplane 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 80 km/h (height increase per unit time). if the plane's airspeed is 550 km/h and there is a wind blowing 90 km/h to the northwest, what is the ground speed of the plane? use \mathbf{v} to denote the plane's speed vector with respect to earth (i. e., the 3d velocity vector measured by the control tower's radars), \mathbf{v}_\text{air} to denote the air speed vector (i. e. the speed with respect to air measured by the pilots), and \mathbf{w} to denote the wind speed vector. start by writing a relationship between these three velocity vectors, and write their components (known and unknown). use the available information to determine the unknowns. hints: the ground velocity vector is the projection onto the earth's surface of the plane's velocity vector \mathbf{v}. you can picture the problem as a plane moving within an air volume, that is itself in translation with respect to earth because of the wind. ground speed =