Chapter 4.4, Problem 39PPE

To determine

To find: the time it does take for the acorn to hit the ground, and to find an answer between two consecutive whole number values of $t$ using graph.

Answer to Problem 39PPE

Acorn hit to the ground in 3 seconds.

Explanation of Solution

Given information:

The height $h$ , in feet, of an acorn that falls from a branch 100 ft above the ground depends on the time $t$ in seconds, since it has fallen. This is represented by the rule $h=100-16t^2$ .

Calculation:

Consider height of acorn is represented by $h$ and time taken acorn to fall is represented by $t$ .

Since $h$ depends on $t$ . So this gives function rule

  $h=100-16t^2$

Solve this function rule for $t$ .

  $\begin{array}{c}h=100-16t^2\\ h+16t^2=100\\ 16t^2=100-h\\ t^2=-\frac{1}{16}h+\frac{100}{16}\\ t=-\frac{1}{4}\sqrt{h}+\frac{10}{4}\end{array}$

Since branch is 100 feet above the ground. In order to make table of values choose different values for $h$ and solve for $t$ . Table is as follows -

$h$	0	100
$t$	2.5	0

Graph each ordered pair $\left(h,t\right)$ . Graph is as follows. In this graph horizontal axis represents time and vertical axis represents height -

  

Observe the graph. Locate origin found that, for height zero time is 2.5.

Thus, acorn hit to the ground in 3 seconds.