Chapter 11.2, Problem 61E

To determine

To find: the velocity of freefalling object when time is at $1$ second.

Answer to Problem 61E

The velocity after $1$ second is $-32\text{feet}/\text{sec}$ .

Explanation of Solution

Given:

Time is at $1$ second.

The velocity at time $t=a$ is:

  $\underset{t\to a}{\lim }\frac{s\left(a\right)-s\left(t\right)}{a-t}$ .

Concept used:

Describe the behavior of $g\left(x\right)$ to the immediate left of $x=a$ .

The left-hand limit at $x=a$ is:

  $\underset{x\to a^{-}}{\lim }g\left(x\right)$ .

Describe the behavior of $g\left(x\right)$ to the immediate right of $x=a$ .

The right-hand limit at $x=a$ is:

  $\underset{x\to a^{+}}{\lim }g\left(x\right)$ .

Give the precise value of $g\left(x\right)$ take at $x=a$ .

Calculation:

Substituting $1$ for $a$ in the equation, it get that the velocity after $1$ second is:

  $\begin{array}{l}\underset{t=1}{\lim }\frac{-16{\left(1\right)}^2+128-\left(-16t^2+128\right)}{1-t}.\\ \Rightarrow \underset{t=1}{\lim }\frac{16\left(t^2-1\right)}{1-t}.\\ \Rightarrow \underset{t=1}{\lim }-16\left(t+1\right).\\ \Rightarrow -32.\end{array}$

Hence, velocity after $1$ second is $-32\text{feet}/\text{sec}$ .