Chapter 5.9, Problem 96E

(a)

To determine

To calculate: The velocity of the object as a function of time when an object is dropped from a height $400\text{ feet}$.

(b)

To determine

To calculate: The position of the object as a function of time when an object is dropped from a height $400\text{ feet}$.

(c)

To determine

To prove: The velocity of the object as a function of time, $v\left(t\right)=-\sqrt{32/k}\tanh \left(\sqrt{32k}t\right)$ when an object is dropped from a height $400\text{ feet}$.

(d)

To determine

To calculate: The limit of velocity that is $\underset{t\to \infty }{\lim }v\left(t\right)$ and its interpretation.

(e)

To determine

To calculate: The position $s$ of the object as a function of time. Also, draw the graph of the position vector in parts (b) and (c) when $k=0$. The additional time required for the object to reach ground level when air resistance is not neglected.

(f)

To determine

The description when the value of $k$ increases. Then test ascertain at a particular value of k.