Chapter 9.4, Problem 53E

a.

To determine

To determine the maximum height of the football .

Answer to Problem 53E

The maximum value of $h=36$ .

Explanation of Solution

Given:

Equation:

  $h=-16t^2+48t$

Concept Used:

Maximum or minimum value of the function

Calculation:

On comparing the equation $a{x}^2+bx+c$ ,

  $a=-16,b=48,c=0$

Since , $a<0$

The function has minimum value.

For minimum value,

Calculate $t$ ,

  $t=\frac{-b}{2a}$

Therefore ,

  $t=\frac{-(48)}{2(-16)}$

So,

  $t=\frac{-48}{-32}$

On substituting $t=\frac{3}{2}$ in equation.

  $h=-16{(\frac{3}{2})}^2+48(\frac{3}{2})$

On squaring,

  $h=-16(\frac{9}{4})+48(\frac{3}{2})$

On solving,

  $h=-4(9)+24(3)$

Therefore ,

  $h=36$

b.

To determine

To determine the axis of symmetry .

Answer to Problem 53E

The axis of symmetry, $t=\frac{3}{2}$

Explanation of Solution

Given:

Equation:

  $h=-16t^2+48t$

Concept Used:

Formula for axis of symmetry, $t=\frac{-b}{2a}$ .

Calculation:

On comparing the equation $a{x}^2+bx+c$ ,

  $a=-16,b=48,c=0$

Calculate the axis of symmetry,

  $t=\frac{-b}{2a}$

Therefore ,

  $t=\frac{-(48)}{2(-16)}$

So,

  $t=\frac{-48}{-32}$

The axis of symmetry, $t=\frac{3}{2}$