How Do You Calculate the Dynamics of Saturn V's Launch?

[leanh6790]

The rocket, named Saturn V, was used to place humans on the surface of the Moon. It has 3 separate stages with the crew Command Module and Lunar Lander on the top. The first stage has a mass of 2 286 688 kg at launch. The stage was powered by 5 F-1 rocket engines which produced a total of 34 596 738 N of thrust at lift-off, and 41 050 866 N just before first stage shut-off. The 5 engines consumed fuel at the rate of 13 347.5 kg per second for the entire 2 minutes and 42 seconds of Stage I burn.
Stage II had a mass of 482 009 kg full and had 5 J-2 engines that put out 4 999 153 N of thrust at ignition and 5 272 819 N just before engine cut-off. One engine shuts down at 4 minutes and 57 seconds, reducing the thrust by 20%, while the remaining 4 engines burn for a total of 6 minutes and 26 seconds. During that time the mass of Stage II drops to 34 464 kg.
Stage III had a mass of 119 123 kg at ignition and 11 386 kg at engine cut-off, 135 seconds later. The third stage had one J-2 engine that put out 803 498 N of thrust at ignition and 940 942 N and cut-off.
An interstage between Stage III and the command module had a mass of 3 652 kg.
The launch control Instrument Unit had a mass of 1 943 kg. The Command Module had a mass of 5 620 kg. The crew Service Module had a mass of 23 229 kg, and the Lunar Module had a mass of 15 147 kg.
At the end of Stage I burn, the Saturn V was 65 837 meters high and 93 269 meters downrange from the Kennedy Space Center at Cape Canaveral, Florida.

FIND THE FOLLOWING:

1. Acceleration at lift-off.
2. Acceleration at end of Stage I burn.
3. Velocity at end of Stage II burn.
4. Acceleration at beginning at Stage II burn.
5. Acceleration at end of Stage II burn.
6. Velocity at end of Stage II burn.
7. Acceleration at beginning of Stage III burn.
8. Acceleration at end of Stage III burn.
9. Velocity at Orbital Insertion.
10. Angle from the vertical during Stage I burn.
11. Actual distance traveled during Stage I burn.
12. Approximate landing point of the discarded Stage I.

 

[D H]

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