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 = 66.0 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 55.0% of the total mass at launch. Assuming constant gravitational acceleration, how long does it take the rocket to achieve maximum upward acceleration?

Answer 1

Suppose mass is ejected at x kg/s.
That gives the rocket a change in momentum, ie a force, of 66x kg m/s/s.

F=66x kgm/sec^2
The initial acceleration is zero, so this force equals the gravitational force Mg.

66x= Mg

x= M×9.8/(66)
x = 0.148 M kg/s

The constant force will provide more and more acceleration as the mass of the rocket decreases.
The maximum upward acceleration occurs right before the rocket runs out of fuel.
0.55M / x = 0.55M/(0.1484M)= 3.70 s .....Ans.

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