Chapter 9.2, Problem 54E

a.

To determine

To calculate height of football each second.

Answer to Problem 54E

  

Explanation of Solution

Given information:

Function of height( h ) is

  $h=-16t^2+40t+5$

Calculation:

Height for each seconds is given in table

  

b.

To determine

To calculate time when height is 15 feet.

Answer to Problem 54E

  $t\approx 2.21825\sec$

  $t\approx 0.2817\sec$

Explanation of Solution

Given information:

Function of height( h ) is

  $h=-16t^2+40t+5$

Calculation:

  $h=-16t^2+40t+5$

As $h=15$

Then

  $15=-16t^2+40t+5$

On solving,

  $16t^2-40t+10=0$

On solving,

  $8t^2-20t+5=0$

On solving,

  $t=\frac{-(-20)\pm \sqrt{{(-20)}^2-4(8)(5)}}{2(8)}$

On solving,

  $t=\frac{20\pm \sqrt{400-160}}{16}$

On solving,

  $t=\frac{20\pm \sqrt{240}}{16}$

On solving,

  $t=\frac{20\pm 4\sqrt{15}}{16}$

On solving,

  $t=\frac{5\pm \sqrt{15}}{4}$

On solving,

  $t=\frac{5+\sqrt{15}}{4}$

  $t=\frac{5-\sqrt{15}}{4}$

On solving,

  $t\approx 2.21825\sec$

  $t\approx 0.2817\sec$

c.

To determine

To calculate time when height is 15 feet.

Answer to Problem 54E

At $t\approx 2.21825\sec$ and $t\approx 2.21825\sec$ height is $15ft$

Explanation of Solution

Given information:

Function of height( h ) is

  $h=-16t^2+40t+5$

Calculation:

  $h=-16t^2+40t+5$

Substituting $t=0$

  $h=-16{(0)}^2+40(0)+5$

On solving,

  $h=5$

Substituting $t=\frac{5}{4}$

  $h=-16{(\frac{5}{4})}^2+40(\frac{5}{4})+5$

On solving,

  $h=30$

Substituting $t=2$

  $h=-16{(2)}^2+40(2)+5$

On solving,

  $h=21$

Table

  

Graph

  

Using graph

At $t\approx 2.21825\sec$ and $t\approx 2.21825\sec$ height is $15ft$