Chapter 8.5, Problem 46PPS

a.

To determine

Find the expression that represents the height in factored form.

Answer to Problem 46PPS

The factored form are $t=0,t=\raisebox{1ex}{$33$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ .

Explanation of Solution

Given: It is given in the question that $10$ inch firework shell is fired from ground level. The height of the shell in feet can be modeled by the expression $h=264t-16t^2$ , where t is the time in seconds after launch.

Concept Used:

In this, use the concept of factorization of the expression.

Calculation: Here, the expression is $h=264t-16t^2$ .

  $\begin{array}{l}h=264t-16t^2\\ h=8t(33-2t)\end{array}$

Put $h=0$ ,

  $\begin{array}{l}8t(33-2t)=0\\ (8t=0),(33-2t=0)\\ t=0,t=\raisebox{1ex}{$33$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\end{array}$

Conclusion:

The factored form are $t=0,t=\raisebox{1ex}{$33$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ .

b.

To determine

Find the height of the shell $0$ seconds and $16.5$ seconds after launch.

Answer to Problem 46PPS

The height at $t=0$ & $t=16.5$ are 0 and $0.8inch$ .

Explanation of Solution

Given: It is given in the question that $10$ inch firework shell is fired from ground level. The height of the shell in feet can be modeled by the expression $h=264t-16t^2$ , where t is the time in seconds after launch.

Concept Used:

In this, use the concept of putting the value in the expression and get the answer.

Calculation: Here, put $t=0$ ,

  $\begin{array}{l}h=264t-16t^2\\ $ h=264(0)-16{(0)}^2$h=0\end{array}$

Now, put $t=16.5$

  $\begin{array}{l}h=264t-16t^2\\ $ h=264(16.5)-16{(16.5)}^2$h=4356-4355.2\\ h=0.8inch\end{array}$

Conclusion:

The height at $t=0$ & $t=16.5$ are 0 and $0.8inch$ .

c.

To determine

Find the position of the shell at $0$ seconds and $16.5$ seconds.

Answer to Problem 46PPS

The height at $0$ seconds is the shell is at the ground.

And the height at $16.5$ seconds the shell is at $0.8inch$ above the ground.

Explanation of Solution

Given: It is given in the question that $10$ inch firework shell is fired from ground level. The height of the shell in feet can be modeled by the expression $h=264t-16t^2$ , where t is the time in seconds after launch.

Concept Used:

In this, use the concept of understanding the position in right way.

Calculation: Here, the height at $0$ seconds is 0 and the height at $16.5$ seconds are $0$ and $0.8inch$ .

Therefore, the height at $0$ seconds is the shell is at the ground.

And the height at $16.5$ seconds the shell is at $0.8inch$ above the ground.

Conclusion:

The height at $0$ seconds is the shell is at the ground.

And the height at $16.5$ seconds the shell is at $0.8inch$ above the ground.

d.

To determine

Find the height of the shell at $8.25\sec$ .

Answer to Problem 46PPS

The height of the shell is $1090inch$ .

Explanation of Solution

Given: It is given in the question that $10$ inch firework shell is fired from ground level. The height of the shell in feet can be modeled by the expression $h=264t-16t^2$ , where t is the time in seconds after launch.

Concept Used:

In this, use the concept of putting the value in the expression and get the answer.

Calculation:

Here, the expression is $h=264t-16t^2$ .

Now, put $t=8.25\sec$ ,

  $\begin{array}{l}h=264t-16t^2\\ $ h=264(8.25)-16{(8.25)}^2$h=2178-1088\\ h=1090inch\end{array}$

Conclusion:

The height is $1090inch$ .