Chapter 9, Problem 9STP

To determine

To find: whether how long after the football is kicked does it hit the ground..

Answer to Problem 9STP

The time will be of $2$ seconds.

Explanation of Solution

Given information:

The given statement is a ball is kicked upward at the velocity of $32$ feet per second.

Calculation:

A placekicker kicks a ball upward with a velocity of $32$ feet per second.

  $v_0=32$ ft/s

The height of an object after $t$ seconds is modeled by the following quadratic equation,

  $h\left(t\right)=v_0\times t-16t^2$........$\left(1\right)$

Substitute $v_0=32$ ft/s in the above equation, the equation that models tha height of the ball will be,

  $h\left(t\right)=32t-16t^2$........ $\left(2\right)$

Compute the time after the football is kicked , it hits the ground, substitute $h=0$ in equation $\left(2\right)$

  $h(t)=32t-16t^2$ and solve for $t$ ,

  $0=32t-16t^2$

  $16t^2-32t=0$

  $\begin{array}{c}16t\left(t-2\right)=0\\ t\left(t-2\right)=0\end{array}$

Apply zero product property,

  $\begin{array}{c}t=0\\ t-2=0\\ t=2\end{array}$

The time $t=0$ represents when the kicker kicks the ball .so, the solution of the equation

  $16t\left(t-2\right)=0$ is $t=2$

Therefore, after $2$ seconds of the ball is kicked, it hits the ground.