Chapter 1.5, Problem 8P

Solution

To find: How long does it take for the shellfish to hit the ground.

The shellfish to hits the ground in $1.369$ seconds.

Given information:

The bird flying at a height of $30$ feet.

Calculation:

Using a table:

Write an equation that models the situation using the height function:

  $h=-16t^2+h_0$

Substitute $h=0$ and $h_0=30$ in the above equation:

  $0=-16t^2+30$

Make a table of values for the function. Set the table so that the value of $t$ start at $0$ and increase in increments of $0.1$ .

Through the table to find the time $t$ at which the height $h$ is $0$ feet.

$t$	$h=-16t^2+30$
$0$	$30$
$0.1$	$29.84$
$0.2$	$29.36$
$0.3$	$28.56$
$0.4$	$27.44$
$0.5$	$26$
$0.6$	$24.24$
$0.7$	$22.16$
$0.8$	$19.76$
$0.9$	$17.04$
$1.0$	$14$
$1.1$	$10.64$
$1.2$	$6.96$
$1.3$	$2.96$
$1.4$	$-1.36$
$1.5$	$-6$
$1.6$	$-10.96$

The table shows that $h=0$ between $t=1.3$ and $t=1.4$ because $h$ has a change of sign from positive to negative.

Therefore, the shellfish hits the ground between $1.3$ and $1.4$ seconds after it is dropped.

Using a graph:

Write an equation that models the situation using the height function:

  $h=-16t^2+h_0$

Substitute $h=0$ and $h_0=30$ in the above equation:

  $0=-16t^2+30$

Enter the function $h=-16t^2+30$ into a graphing calculator.

  

Graph the height function. The positive $t-$ value for which $h=0$ using the zero feature. The graph shows that $h=0$ when $t=1.369$ .

Therefore, the shellfish hits the ground $1.369$ seconds after if it dropped.