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Math Project!  <br />Rachel Carrillo<br />Marian Hsiung<br />Natalia Castro<br />Holly Qiu<br />Period A & 5<br />May, 20...
Problem<br />Pg. 162 #14<br />An astronaut standing on the moon throws a rock into the air, the height of the rock is<br /...
a.) Find the expression for the velocity and acceleration of the rock.<br />Original equation: s(t)= -(27/10)t2 + 27t + 6<...
b.)Find the time when the rock is at its highest point by finding the time when the velocity is zero. What is the height o...
c.)How does the acceleration of the rock compare with the acceleration due to gravity of earth?<br />The gravity of earth ...
What causes Gravity to differ?<br />Gravity is the attractions between objects. It is directly correlated with mass.<br />...
Across the Universe<br />By finding the gravity/acceleration of each planet and integrating it, given an initial condition...
Mercury<br />Gravity: 12.22 ft/s2<br />A(t)=12.22<br />∫ A(t) dt= 12.22t+C=V(t)<br />V(0)=10<br />V(t)= 12.22t+10<br />∫V(...
Venus<br />Gravity: 28.2ft/s²<br />A(t)=28.2<br />∫ A(t) dt=28.2t+C=V(t)<br />V(0)=10<br />V(t)=28.2t+10<br />∫V(t) dt=14....
Mars<br />Gravity: 12.22 ft/s2<br />A(t)=12.22<br />∫ A(t) dt= 12.22t+C=V(t)<br />V(0)=10<br />V(t)= 12.22t+10<br />∫V(t) ...
Jupiter<br />Gravity: 81.75 ft/s²<br />A(t)=81.75<br />∫ A(t) dt= 81.75t+C=V(t)<br />V(0)=10<br />V(t)=81.75t+10<br />∫V(t...
Saturn<br />Gravity: 10.584 ft/s²<br />A(t)=10.584<br />∫ A(t) dt=10.584t+C=V(t)<br />V(0)=10<br />V(t)=10.584t+10<br />∫V...
Uranus<br />Gravity: 28.2ft/s²<br />A(t)=28.2<br />∫ A(t) dt=28.2t+C=V(t)<br />V(0)=10<br />V(t)=28.2t+10<br />∫V(t) dt=14...
Pluto (YES, it IS a planet)<br />Gravity: 25.722 ft/s²<br />A(t)=25.722<br />∫ A(t) dt=25.722t+C=V(t)<br />V(0)=10<br />V(...
Another Example is…..<br />
Problem with Weight and Height<br />Pg. 134, number 35<br />Problem: To estimate the height of a building, a weight is dro...
Answer<br />S(t)= -16t2 + s0<br />S(9.2)= -16(9.2)2 + s0<br /> s0 =1354.24 ft<br />
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Math Project

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Math Project

  1. 1. Math Project!  <br />Rachel Carrillo<br />Marian Hsiung<br />Natalia Castro<br />Holly Qiu<br />Period A & 5<br />May, 2010<br />
  2. 2. Problem<br />Pg. 162 #14<br />An astronaut standing on the moon throws a rock into the air, the height of the rock is<br /> s(t)= -(27/10)t2 + 27t + 6<br />Where s(t) is measured in feet and t is measured in seconds.<br />a.) Find the expression for the velocity and acceleration of the rock.<br />b.)Find the time when the rock is at its highest point by finding the time when the velocity is zero. What is the height of the rock at this time?<br />c.)How does the acceleration of the rock compare with the acceleration due to gravity of earth?<br />
  3. 3. a.) Find the expression for the velocity and acceleration of the rock.<br />Original equation: s(t)= -(27/10)t2 + 27t + 6<br /> s’’(t) = v’(t) = a(t)<br />V(t)= s’(t)= -(27/10)(2)t + 27(1) = 6(0)<br />= -(27/5)t + 27 in ft/sec<br />A(t)= s’’(t)= -(27/5) ft/sec2 (constant acceleration)<br />
  4. 4. b.)Find the time when the rock is at its highest point by finding the time when the velocity is zero. What is the height of the rock at this time?<br />-(27/5)t + 27 =0 t=5<br />S(5)=73.5 ft<br />
  5. 5. c.)How does the acceleration of the rock compare with the acceleration due to gravity of earth?<br />The gravity of earth is -32.1740 ft/s2<br />The gravity of the moon is –(27/5) ft/s2<br />The acceleration of the moon is less than the Earth’s therefore, the gravity pull on earth is stronger.<br />
  6. 6. What causes Gravity to differ?<br />Gravity is the attractions between objects. It is directly correlated with mass.<br />Mass:<br /> Jupiter > Earth > Moon Therefore<br />Gravity: <br /> Jupiter > Earth > Moon<br />
  7. 7. Across the Universe<br />By finding the gravity/acceleration of each planet and integrating it, given an initial condition, we can predict the maximum height the rock would reach if thrown in every planet.<br />∫ A(t) dt= V(t)<br />∫ V(t) dt= S(t)<br />Given:<br />The rock is thrown with an initial velocity of 10 ft/sec.<br />The astronaut is 6 ft high.<br />
  8. 8. Mercury<br />Gravity: 12.22 ft/s2<br />A(t)=12.22<br />∫ A(t) dt= 12.22t+C=V(t)<br />V(0)=10<br />V(t)= 12.22t+10<br />∫V(t) dt= 6.11t2 +10t+C=S(t)<br />S(0)= 6<br />S(t)= 6.11t2 +10t+6<br />
  9. 9. Venus<br />Gravity: 28.2ft/s²<br />A(t)=28.2<br />∫ A(t) dt=28.2t+C=V(t)<br />V(0)=10<br />V(t)=28.2t+10<br />∫V(t) dt=14.1t²+10t+C=S(t)<br />S(0)=6<br />S(t)=14.1t²+10t+6<br />
  10. 10. Mars<br />Gravity: 12.22 ft/s2<br />A(t)=12.22<br />∫ A(t) dt= 12.22t+C=V(t)<br />V(0)=10<br />V(t)= 12.22t+10<br />∫V(t) dt= 6.11t2 +10t+C=S(t)<br />S(0)= 6<br />S(t)= 6.11t2 +10t+6<br />
  11. 11. Jupiter<br />Gravity: 81.75 ft/s²<br />A(t)=81.75<br />∫ A(t) dt= 81.75t+C=V(t)<br />V(0)=10<br />V(t)=81.75t+10<br />∫V(t) dt=40.875t²+10t+C=S(t)<br />S(0)=6<br />S(t)=40.875t²+10t+6<br />
  12. 12. Saturn<br />Gravity: 10.584 ft/s²<br />A(t)=10.584<br />∫ A(t) dt=10.584t+C=V(t)<br />V(0)=10<br />V(t)=10.584t+10<br />∫V(t) dt=5.292t²+10t+C=S(t)<br />S(0)=6<br />S(t)=5.292t²+10t+6<br />
  13. 13. Uranus<br />Gravity: 28.2ft/s²<br />A(t)=28.2<br />∫ A(t) dt=28.2t+C=V(t)<br />V(0)=10<br />V(t)=28.2t+10<br />∫V(t) dt=14.1t²+10t+C=S(t)<br />S(0)=6<br />S(t)=14.1t²+10t+6<br />
  14. 14. Pluto (YES, it IS a planet)<br />Gravity: 25.722 ft/s²<br />A(t)=25.722<br />∫ A(t) dt=25.722t+C=V(t)<br />V(0)=10<br />V(t)=25.722t+10<br />∫V(t) dt=12.861t²+10t+C=S(t)<br />S(0)=6<br />S(t)=12.861t²+10t+6<br />
  15. 15. Another Example is…..<br />
  16. 16. Problem with Weight and Height<br />Pg. 134, number 35<br />Problem: To estimate the height of a building, a weight is dropped from the top of the building into a pool at ground level. How high is the building if the splash is seen 9.2 seconds after the weight is dropped?<br />
  17. 17. Answer<br />S(t)= -16t2 + s0<br />S(9.2)= -16(9.2)2 + s0<br /> s0 =1354.24 ft<br />

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