Just before it landed on the moon, the Apollo 12 lunar lander had a mass of 1.4×104 kg. What rocket thrust was necessary to have the lander touch down with zero acceleration?

Explanation:

For a lunar lander acceleration in an upward direction, the net force that acts on it can be expressed as:

The equation for the net force that acts on the lunar lander is:

For the lander touch down to be zero acceleration, it implies that the acceleration of the moving rocket is zero(a free body fall)

i.e. a = 0

We can now regard the Apollo 12 lunar as a freely falling body

However; the force of gravity as a result of the moon acting on the lunar rocket is:

Then; the equation for the thrust force of the lunar rocket is:

Finally; the thrust force of the lunar rocket can be determined as:

Acceleration due to gravity ot the surface of the moon = 1.625 m/s²

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