A rocket is launched vertically up with no initial velocity. Propulsion is provi

Question

A rocket is launched vertically up with no initial velocity. Propulsion is provided by the ejection of mass with constant velocity of ejection u = 54.0 m/s relative to the rocket and at a constant rate so determined that the initial acceleration is zero. The mass of fuel that can be ejected is 79.0% of the total mass at launch. Assuming constant gravitational acceleration, how long does it take the rocket to achieve maximum upward acceleration?

hint: The constant ejection of mass from the rocket is equivalent with an instantaneous inelastic collision. The momentum-impulse theorem in the presence of the gravitational force can be used. Consider g = 9.81 m/s2.

please show all steps and equations.thanks for your help

Explanation / Answer

initial acceleration is zero:

==> M0 g = u dM/dt

==> dM/dt = M0 g/u = (9.81/54) * M0 = 0.18167 M0

M_fuel = (dM/dt) t = 0.18167 M0 t

0.18167 M0 t = 0.79 M0

==> 0.18167 t = 0.79

==> t = 4.35 s

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