Coughing forces the trachea to contract, which affects the velocity v of the air passing through the trachea. suppose the velocity of the air during coughing is v = k(r-r)r2 where k and r are constants, r is the normal radius of the trachea, and r is the radius during coughing. what radius will produce the maximum air velocity?

1point) a skydiver weighing 130 lb (including equipment) falls vertically downward from an altitude of 14,000 ft and opens the parachute after 20 s of free fall. assume that the force of air resistance, which is directed opposite to the velocity, is of magnitude 0.85|v|0.85|v| when the parachute is closed and is of magnitude 17|v|17|v| when the parachute is open, where the velocity vv is measured in ft/s. assume that acceleration due to gravity has magnitude 32 ft/s/s; remember that weight is the product of mass and gravitational acceleration. find the speed of the skydiver when the parachute opens. speed is 150.6121788 ft/s find the skydiver's height when the parachute opens. height is 2338.98591 ft find the limiting velocity vlvl after the parachute opens. (think about whether this should be positive or negative.) vl=vl= 7.647 ft/s

Abaseball is thrown from the outfield toward the catcher. when the ball reaches its highest point, which statement is true? (a)its velocity is not zero, but its acceleration is zero. (b) its velocity and its acceleration are both zero. (c) its velocity is perpendicular to its acceleration. (d) its acceleration depends on the angle at which the ball was thrown. (e) none of the above statements are true.

A2.50 × 105 w motor is used for 26.4 s to pull a boat straight toward shore. how far does the boat move toward shore if a force of 4.20 × 104 n is applied by the motor?