Chapter 8.2, Problem 46PPS

(a)

To determine

To find: The equation of the height of the shell in factored form.

Answer to Problem 46PPS

The required equation is $f\left(x\right)=263t-16t^2$ .

Explanation of Solution

Given information:

The given equation of height is

  $h=263t-16t^2$

Consider the given equation of height is

  $h=263t-16t^2$

Substitute $f\left(x\right)$ for h in the above equation.

  $f\left(x\right)=263t-16t^2$

Hence, the required equation is $f\left(x\right)=263t-16t^2$ .

(b)

To determine

To find: The time when the height of the shell is zero.

Answer to Problem 46PPS

The required time at zero height is $16.44\sec$ .

Explanation of Solution

Given information:

The given equation of height is

  $h=263t-16t^2$

Calculation:

Consider the given equation of height is

  $h=263t-16t^2$

Substitute $0$ for h in the above equation.

  $\begin{array}{l}0=263t-16t^2\\ t\left(263-16t\right)=0\\ t=0or263-16t=0\end{array}$

Solve the equation $263-16t=0$ to find the value of t .

  $\begin{array}{c}16t=263\\ t=\frac{263}{16}\\ =16.44\end{array}$

Hence, the required time at zero height is $16.44\sec$ .

(c)

To determine

To calculate: The height of the shell at $8\sec$ and $10\sec$ .

Answer to Problem 46PPS

The required of the shell at $8\sec$ and $10\sec$ is $1080\text{ft}$ and $1030\text{ft}$ .

Explanation of Solution

Given information:

The given equation of height is

  $h=263t-16t^2$

Calculation:

Consider the given equation of height is

  $h=263t-16t^2$

Substitute $8\sec$ for t in the above equation.

  $\begin{array}{c}h=263\times 8-16\times 8^2\\ =1080\text{ft}\end{array}$

Substitute $10\sec$ for t in the above equation.

  $\begin{array}{c}h=263\times 10-16\times {10}^2\\ =1030\text{ft}\end{array}$

Hence, the required of the shell at $8\sec$ and $10\sec$ is $1080\text{ft}$ and $1030\text{ft}$ .

(d)

To determine

To calculate: The raise or fall of the shell at $10\sec$ .

Answer to Problem 46PPS

The required height started falling at $10\sec$ .

Explanation of Solution

Given information:

The given equation of height is

  $h=263t-16t^2$

Calculation:

Consider the given equation of height is

  $h=263t-16t^2$

Substitute $10\sec$ for t in the above equation.

  $\begin{array}{c}h=263\times 10-16\times {10}^2\\ =1030\text{ft}\end{array}$

It is seen that the height started falling at $10\sec$ as at $8\sec$ the height is more than $1030\text{ft}$ .

Hence, the height started falling at $10\sec$ .