Chapter 4.2, Problem 77E

( a)

To determine

To calculate:The tabulated values of height, $h$, when the ball from the ground level is kicked upwards with the initial velocity of $48\text{ feet per second}$ such that, the height as a function of time is represented as $h\left(t\right)=-16t^2+48t$ for $0\le t\le 3$,

$\begin{array}{cccccccc}t& 0& 0.5& 1& 1.5& 2& 2.5& 3\\ h& & & & & & & \end{array}$

and determine whether the ball reaches the height of $64\text{ feet}$ or not as given below.

( b)

To determine

Whether the ball reaches a height of $64\text{ feet}$ or not when the height as a function of time is represented as $h\left(t\right)=-16t^2+48t$ for $0\le t\le 3$, algebraically.

( c)

To determine

To graph:The provided function $h\left(t\right)=-16t^2+48t$, and determine graphically whether the ball reaches the height of $64\text{ feet}$ or not.

( d)

To determine

The comparison between the results obtained in part $\left(\text{a}\right),\left(\text{b}\right)\text{ and }\left(\text{c}\right)$ for the ball to reach a height of $64\text{ feet}$, when the height with respect to time function is given as $h\left(t\right)=-16t^2+48t$ for $0\le t\le 3$.