Q. 12 - Calculus

Question

An orange falling from 20 feet has a height of $s\left(t\right)=20-16t^2$ feet when it has fallen for t seconds.

(a) Graph the position function s(t) and find the time that the orange will hit the ground. 

(b) Make a table to record the average rates that the orange is falling during the last second, half-second, quarter-second, and eighth-of-a-second of its fall. 

(c) From the data in your table, make a guess for the instantaneous final velocity of the orange at the moment it hits the ground 

Step-by-Step Solution

Answer

part (a) Step 1. Given information

Given is:

An orange falling from 20 feet has a height of $s\left(t\right)=20-16t^2$ feet when it has fallen for t seconds.

We have to graph the position function.

Make a table to record the average rates 

Make a guess for the instantaneous final velocity of the orange at the moment it hits the ground 

Part (a) Step 2. Make a graph

Given function is:

$s\left(t\right)=20-16t^2$

The graph of the function is;

At t=1.118, the orange will hit the ground.

Part (b) Step 1. Make a table

Table to record the average rates that the orange is falling during the last second, half-second, quarter-second, and eighth-of-a-second of its fall is:

t	$1$	$\frac{1}{2}$	$\frac{1}{4}$	$\frac{1}{8}$
s(t)	4	16	19	$\frac{79}{4}$

Part (c) Step 1. Final velocity

From the data in the table, we can estimate -19.75 feet per second on impact it hits the ground.