Exercise 12 — Active Calculus

A bungee jumper's height $h$ (in feet ) at time $t$ (in seconds) is given in part by the table:

$t$	$0.0$	$0.5$	$1.0$	$1.5$	$2.0$	$2.5$	$3.0$	$3.5$	$4.0$	$4.5$	$5.0$
$h(t)$	$200$	$184.2$	$159.9$	$131.9$	$104.7$	$81.8$	$65.5$	$56.8$	$55.5$	$60.4$	$69.8$

$t$	$5.5$	$6.0$	$6.5$	$7.0$	$7.5$	$8.0$	$8.5$	$9.0$	$9.5$	$10.0$
$h(t)$	$81.6$	$93.7$	$104.4$	$112.6$	$117.7$	$119.4$	$118.2$	$114.8$	$110.0$	$104.7$

Use the given data to estimate $h'(4.5)$ , $h'(5)$ , and $h'(5.5)$ . At which of these times is the bungee jumper rising most rapidly?
Use the given data and your work in (a) to estimate $h''(5)$ .
What physical property of the bungee jumper does the value of $h''(5)$ measure? What are its units?
Based on the data, on what approximate time intervals is the function $y = h(t)$ concave down? What is happening to the velocity of the bungee jumper on these time intervals?

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