Question

QB: The Rocket Equation
The velocity of a rocket t seconds after liftoff from earth can be modeled by
v(t) = -g*t - v_e * Ln( (m-r*t)/m )
where
g = 9.8 m/s^2, the usual earth gravity value,
v_e = exhaust velocity, 3000 m/s (the e here isn't related to 2.71828...)
m = initial mass of the rocket+fuel: 30,000 kg
r = rate of using fuel = 160 kg/s
i) Find a formula for the acceleration function a(t) and graph it, t=0 to 60. Do the formula work by hand, but not the graphing, of course.
ii) Find a formula for the jerk function j(t) = a'(t) and graph it, t=0 to 60. Do the formula work by hand, but not the graphing.

Answer 1

c) Accelation

D 10 5 20 0 10 30 40 50 time(seconds)->

6 Tek function ) d) 30000-l6ot) 沺ー 76800000 Css) (80000-160t) ct) Graph

0.2 ︶ 0.15 0-1 0:05 40 30 50 60 0 10 20 time(seconds)->