Aplane is heading due north: its nose points towards the north direction, but its trajectory on the ground deviates from the north direction due to a sideways component of the wind. the plane is also climbing at the rate of 120 km/h (height increase per unit time). if the plane's airspeed is 470 km/h and there is a wind blowing 80 km/h to the northwest, what is the ground speed of the plane? use 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), vair to denote the air speed vector (i. e. the speed with respect to air measured by the pilots), and 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. assume that the x axis is oriented toward the east, the y axis is oriented toward the north, and the z axis is vertical, oriented toward the sky. hints: the ground velocity vector is the projection onto the earth's surface of the plane's velocity vector 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. once you have determined all the unknowns, enter the components of the vectors w, vair. and v within angle brackets typset with 'and> , using exact values or 4 decimal place accuracy: t w vair ground speed enter your answ er as a number (not a vector), using exact values or at least 4 decimal place accuracy.