Chapter 8.2, Problem 11E

a.

To determine

To complete:

The given table using given equation.

Answer to Problem 11E

The complete table would be:

t	0	5	10	15	20	25	30
d	0	120	240	360	480	600	720

Explanation of Solution

Given:

In 1997, the pathfinder spacecraft landed on Mars.It contained a robotic vehicle named Sojourner that could roam up to 500 meters from the lander. The distance d (in meters) that Sojourner could travel in t hours in given by $d=24t$ .

t	0	5	10	15	20	25	30
d

Calculation:

To complete our given table, we will substitute the given values of t in our given equation as:

  $\begin{array}{l}d=24t\\ d=24(0)\\ d=0\end{array}$

  $\begin{array}{l}d=24t\\ d=24(5)\\ d=120\end{array}$

  $\begin{array}{l}d=24t\\ d=24(10)\\ d=240\end{array}$

  $\begin{array}{l}d=24t\\ d=24(15)\\ d=360\end{array}$

  $\begin{array}{l}d=24t\\ d=24(20)\\ d=480\end{array}$

  $\begin{array}{l}d=24t\\ d=24(25)\\ d=600\end{array}$

  $\begin{array}{l}d=24t\\ d=24(30)\\ d=720\end{array}$

Therefore, the complete table would be:

t	0	5	10	15	20	25	30
d	0	120	240	360	480	600	720

b.

To determine

To graph:

The equation $d=24t$ using the table.

Answer to Problem 11E

The graph of the equation would look like:

Explanation of Solution

Given:

In 1997, the pathfinder spacecraft landed on Mars. It contained a robotic vehicle named Sojourner that could roam up to 500 meters from the lander. The distance d (in meters) that Sojourner could travel in t hours in given by $d=24t$ .

Calculation:

Upon graphing our given equation, we will get our required graph as shown below:

c.

To determine

To find:

The point on the graph whose d-coordinate is 500, and estimate the t -coordinate of this point. How much time would it take Sojourner to reach its maximum distance from the lander?

Answer to Problem 11E

It will take approximately 20.83 hours for Sojourner to reach its maximum height.

Explanation of Solution

Given:

In 1997, the pathfinder spacecraft landed on Mars. It contained a robotic vehicle named Sojourner that could roam up to 500 meters from the lander. The distance d (in meters) that Sojourner could travel in t hours in given by $d=24t$ .

Calculation:

To find the t -coordinate of the point whose d -coordinate is 500, we will substitute $d=500$ in our given equation as shown below:

  $\begin{array}{l}d=24t\\ 500=24t\\ 24t=500\\ \frac{24t}{24}=\frac{500}{24}\\ t=20.833333\\ t\approx 20.83\end{array}$

Therefore, the t -coordinate of the point would be approximately 20.83.

Since Sojourner can roam up to 500 meters from the lander, therefore, it will take approximately 20.83 hours for Sojourner to reach its maximum height.