we got a homework question about the take off of a rocket, its acceleration proportional to fuel usage.
we are given acceleration as:
((d^2)h) / (d(t^2)) = kb / m(subscript 0) - bt[/tex]
Is all of that in the denominator? Is it
?
[tex]where dm/dt = -b refers to (
The rate at which the total mass of the rocket changes with time is equal to the fuel consumption rate)
integrating this function (dm/dt = -b) gives m(t) = -bt + constant, whereby the mass at time (0) = constant = m(subscript 0)
the initial mass of the rocket is m(subscript 0) the initial mass of the fuel is Xm(subscript 0) where X is an unspecified fraction between 0 and 1 A
t some point in time, say at t = t*, the fuel runs out and the
mass of the rocket will be its initial mass minus the initial mass of
fuel. This is described by
m(t*) = -bt* + m0
m(t*) = m0 - X.m0
k is an undefined constant
well we start with the original formula for the acceleration:
((d^2)h) / (d(t^2)) = kb / m(subscript 0) - bt
and i need to integrate this once, to find the velocity at a specific time, and then integrate again to find the height at a specific time