1. Apollo 13
Zack Mayo

2. Premise
After the explosion of the oxygen tanks of the LEM on the apollo 13 mission control has two options. Option 1 where the LEM would turn on the retro rockets and head back home. Option two uses the gravitational pull of the moon to slingshot the astronauts back to Earth. As history shows option 2 was selected and was the right choice. Lets see what might of happend is option 1 was chosen.
What do we do captain?
Mission control says option 1

3. How To Graph? Time(seconds) Distance from moon(KM) 1 425 2 356 3 293
Enter data on calculator, press STAT, then select edit. Make sure plot one is turned on(2nd STATPLOT, 1, select on. Hit graph, then press ZOOM, scroll down to nine and press.

4. What does the data look like?
A steady decline of y values as the x value grows larger( the points get closer to the x axis as the x value gets bigger).

5. Make the Graph Larger
Press window and change the values to these, Xmin=- 5,Xmax=30,Xscl=5,Ymin=-60,Ymax=600,Yscl=100. Now press graph for a larger window.

6. What does the x-axis represent?
The x-axis represents the surface of the moon.

7. Does it look like Apollo 13 hit the moon?
Yes, according to the graph, apollo 13 will crash into the moon.

8. Quadratic Regression Time
Press STAT, move the cursor until CALC, and the select option 5, QuadReg.
What is the value of a? a=3 b? b=-78 and c? c=500.

9. How Well Does The Line Fit The Graph
The line goes through each plotted point on the graph.

10. What is the Minimum Point of the Graph?
78/2(3)
78/6= 13
The minimum point is at 13

11. Does the Model tell that Apollo 13 Crashed into the Moon, just touches the surface, or pulls away before hitting the surface
The model tells that apollo 13 crashes into the moon because the line( the path the rocket takes) goes through the x-axis(the surface of the moon) before it goes back up.
WE’RE GOING TO CRASH!

12. Approximately where is the rocket at t=10 seconds according to the model
The model tells when t= about 10 seconds the distance is about 20 km from the surface of the moon.
No really
We’re getting close

13. For the situation, what is the y-intercept
For the situation, y= is distance from the moon in km.

14. At what time will apollo 13 crash into the moon
Apollo 13 will crash into the moon at about 12 seconds. I found that by looking at the graph and plugging numbers into the formula until y= a negative number.