Chapter 1, Problem 46RE

Suppose that a package of medical supplies is dropped from a helicopter straight down by parachute into a remote area. The velocity $\upsilon$ (in feet per second) of the package $t$ seconds after it is released is given by $\upsilon =24.61\left(1-e^{-1.3t}\right)$ .

(a) Graph $\upsilon$ versus $t$ .

(b) Show that the graph has a horizontal asymptote $\upsilon =c$ .

(c) The constant $c$ is called the terminal velocity. Explain what the terminal velocity means in practical terms.

(d) Can the package actually reach its terminal velocity? Explain.

(e) How long does it take for the package to reach $98\%$ of its terminal velocity?