Chapter 9.2, Problem 16P

A punter kicked the football into the air with an upward velocity of 62 ft/s. Its height $h$ in feet after $t$ seconds is given by the function $h=-16t^2+62t+2.$

What is the maximum height the ball reaches? How long will it take the football to reach the maximum height? How long does it take for the ball to hit the ground?

To determine

To calculate: The maximum height the ball reaches and time taken the football to reach the maximum height and time taken the football to hit the ground.

Answer to Problem 16P

The maximum height the ball reaches $=62.05\text{ feet}$

time taken the football to reach the maximum height $t=1.9\text{ sec}$ .

time taken the football to hit the ground $t=5.8\text{ sec}$ .

Explanation of Solution

Given information: A punter kicked the football into the air with an upward velocity of $62\raisebox{1ex}{$ft$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ .

Its height h in feet after t seconds is given by the function $h=-16t^2+62t+2$ .

Calculation:

height h in feet after t seconds is given by the function $h=-16t^2+62t+2$ .

Graph of function $h=-16t^2+62t+2$

According to the given graph

The maximum height the ball reaches $=62.05\text{ feet}$

and time taken the football to reach the maximum height.

The maximum height the ball reaches $=62.05\text{ feet}$

function $h=-16t^2+62t+2$

Here, $h=62.05\text{ feet}$

  $\begin{array}{l}62.05=-16t^2+62t+2\\ 16t^2-62t+60.05=0\\ t=1.9\text{ sec}\end{array}$

time taken the football to reach the maximum height $t=1.9\text{ sec}$ .

time taken the football to hit the ground.

  $\begin{array}{l}h=0\\ 16t^2-62t-2=0\\ t=3.9\text{ sec}\end{array}$

time taken the football to hit the ground $t=(3.9+1.9)\text{ sec}$ .

time taken the football to hit the ground $t=5.8\text{ sec}$ .