Math Project
- 1. KOREAN MISSILE Moon Shot
- 2. STEPS --Distance from center of Earth to center of Moon. --Radius of Moon (27 % of Earth’s radius) --Proportion for Earth’s radius --Cross multiply --Divide by coefficient for Earth’s radius -- Subtract Earth and Moon’s radius from distance between core of Earth and Moon for miles from surface to surface.
- 3. WORK 238,897 miles 1,079.6 miles 1,079.6/x = 27/100 27x = 107,960 x= 3,998.5 miles 238,897 – 1,079.6 – 3,998.5 = 233,818.9 miles from Earth
- 4. STEPS --Create a scatter plot with each missile’s distance --Find both lines of best fit. --Use calculator to determine the point of intersection.
- 6. STEPS --Convert lines of best fit to standard form. --Set up a system of equations using the lines of best fit. --Solve by substitution for point of intersection --Check the solution
- 7. WORK North Koreans: y = 24388x – 21474 Americans: y = 26,176x – 40,085 (10.408836, 232,376.7) (calculator)
- 8. WORK x = # of days missile traveled y = # miles away from Earth 24,388x –y = 21,474 (North Koreans) 26,176x –y = 40,085 (Americans) Y= 26,176x -40,085
- 9. WORK 24,388x – (26,176x – 40,085) = 21,474 24,388 – 26,176x + 40,085 = 21,474 -1,788x= -18,611 x = 10.408836 x ≈ 10.4 days
- 10. WORK 24,388(10.408836) – y = 21,474 253,850.6924 – y = 21,474 -y = -232,376.6924 y = 232,376.6924 y ≈ 232,376.7 miles from Earth --So about (10.4 , 232,376.7) --The missiles intersect at about 10.4 days and meet at about 232,376.7 miles from Earth.
- 11. 24,388(10.408836) - 232,376.7= 21,474 253,850.7 -232,376.7= 21,474 21,474 = 21,474 26,176(10.408836) – 232,376.7= 40,085 272461.7 – 232,376.7= 40,085 40,085 = 40,085 CHECK
- 12. STEPS --Calculate the miles per hour by dividing the miles per day by the number of hours (24) in a day. --Calculate the kilometers per hour by using the conversion of 1 mile = 1.609344 kilometers with the mph. --Calculate the km/day by taking the km/hr times 24 hours in a day.
- 13. Korean Missile: 24388miles/24 hours = 1,016.17 mph 1,016.17mph(1.609344km) = 1,635.37 km/hr 1635.37km/hr(24hrs) = 39,248.88 km/day WORK
- 14. American Missile: 26,176miles/24 hours = 1,090.67 mph 1090.67mph(1.609344km) = 1,755.26 km/hr 1755.26km/hr(24hrs) = 42,126.24 km/day WORK
- 15. In the race to save the moon, the Americans were successful. It was a very close call as on the 11 th day after the North Koreans launched their missile that was traveling at about 1,635.37 km/h, that the American missile, traveling at about 1,755.26 km/hr, caught up. They collided about 232,376.7 miles from Earth. Thankfully, the moon is located about 233,818.9 miles from Earth on average so the moon was saved on an average day as the American missile intercepted the North Korean Missile just in time to save our moon. Conclusion
- 16. There are few possible errors that could have occurred during calculations. In several cases a decent amount of rounding had to be done, which can throw calculations off a little. However, a major problem could be that the distance of the moon from Earth given by NASA is an average distance. This is because the moon does not follow a circular path; it is actually an elliptical path around Earth. Possible Error
- 17. Therefore at certain times the moon is farther away or closer in relation to the average distance from Earth. So, if the Koreans happened to have shot their missile for the moon when the moon is closer to Earth, the American missile wouldn’t succeed in saving the moon because the moon gets as close as about 221,460 miles from Earth, and their rocket would have intercepted the Koreans behind the moon. Possible Error
- 19. Media Designer: Cody Tyson Mathematical Work: Evan Bittner Calculator Work: Brody Troutman Lead Presenter/Checker/Editor : Frasier Mango