Aperson coughs when a foreign object is in the windpipe. the velocity of the cough depends on the size of the object. supppose a person has a windpipe with a 20-mm radius. if a foreign object has a radius r, in millimeters, then the velocity v, in millimeters/second, needed to remove the object by a cough is given by:

v=(20-r)/s The greater the object, the larger the velocity of the cough. Therefore, since the velocity and the radius of the object have a direct relationship, they must both be in the numerator of the equation. Since velocity is mm/s, time needs to be a part of both sides of the equation to balance it, so it is put in the denominator.