When airplanes land or take off, they always travel along a runway in the direction that is “into” the wind because the “lift force” on an airplane wing depends on the speed of the airplane relative to the air (v_rel). We’ll see in Chapter 10 that the lift force is proportional to v² _rel. Consider a case in which a run way is parallel to the x axis and the wind velocity is v_wind = +20 mi/h (directed along +x). 

(a) In what direction should the airplane travel to take off (along +x or –x)? 

(b) Estimate the speed of a typical airplane (e.g., a Boeing 737) relative to the runway as it takes off. 

(c) Find the ratio of the lift force for an airplane that travels into the wind to the lift force when it travels in the opposite direction. 

(d) Is this factor large enough to make a significant difference?