Gliding falcon: Consider a bird that is gliding straight with a small downward gliding angle between the bird’s path and the horizontal.70 The rate s at which the bird’s altitude decreases is called...

Gliding falcon: Consider a bird that is gliding straight with a small downward gliding angle between the bird’s path and the horizontal.70 The rate s at which the bird’s altitude decreases is called the sinking speed, and it is a function of the airspeed u (the bird’s speed relative to the air). For the laggar falcon (which is similar to the peregrine falcon), one model is

Here s and u are measured in meters per second, and the formula is valid for airspeeds up to 15 meters per second.

a. Make a graph of the sinking speed as a function of the airspeed. Such a graph is called a performance diagram and is often used to study the efficiency of gliders.

b. Express using functional notation the sinking speed when the airspeed is 5 meters per second, and then calculate that value.

c. Explain in practical terms the behavior of the graph near the pole at u = 0.

d. At what airspeed is the sinking speed minimized?