the first stage of a saturn v rocket burned for 2.5 minutes, lifting the rocket

Question

the first stage of a saturn v rocket burned for 2.5 minutes, lifting the rocket to an altitude 42 miles and speed of 6164 per hours and burning 2,000,000 kilogram of propellant.

A) what is tha acceleration of the rocket during this time? express this in terms of g(9.8m/s^2).

B) if the first stage separates at 68 km, how har up do you expect it continue ballistically. ignore air friction and assume the rocket is climbing straight up.

C) if we ignore air friction, how much time will the first stage take to fall back on the earth (in atlantic ocean) after separation?

Explanation / Answer

A) 2ad = v^2 - u^2

v = 6164 mph = 6164 x 1609/3600 = 2754.97 m/s

2 x a x 42 x 1609m   = 2754.97^2

a = 56.16 m/s2 = 5.73g

b) v = srqrt (2ad) = 2763.65 m/s

d = v^2/g = 779363.27 m or 779.36 km

c) h = ut +at^2/2

- 68 x 1000 = 2763.65t - 9.8t^2

4.9t^2 - 2763.65 - 68000= 0

t = 587.63

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