Chapter 11, Problem 26P

The velocity of a skydiver whose parachute is still closed can be modeled by assuming that the air resistance is proportional to the velocity.

From Newton’s second law of motion the relationship between the mass m of the skydiver and his velocity v is given by (down is positive):

$mg-cv=m\frac{dv}{dt}$

where c is a drag constant and g is the gravitational constant (g = 9.81 m/s²).

(a) Solve the equation for v in terms of m, g, c, and i, assuming that the initial velocity of the skydiver is zero.

(h) It is observed that 4 s after a 90-k skydiver jumps out of an airplane, his velocity is 28 in/s. Determine the constant c.

(c) Make a plot of the skydiver velocity as a function of time for $0\le t\le 30$ s.