The Lunar Module could make a safe landing if its vertical velocity at impact is

Question

The Lunar Module could make a safe landing if its vertical velocity at impact is 3.5m/s or less. Use conservation of energy to determine h in each case. The acceleration due to gravity at the surface of the Moon is 1.62 m/s2. Suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is zero. And then suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is 1.6m/s downward.

Explanation / Answer

Use Torricelli's: v2 = u2 + 2as
Take down as positive
(a)
When Moment is zero
(3.5m/s)2 = 0 + 2 * 1.62m/s2 * s
s = 3.78 m

(b)
Moment is 1.6 m/s downwards
(3.5m/s)2 = (1.6m/s)2 + 2 * 1.62m/s2 * s
12.25 = 2.56 + 3.24 * s
s = 2.99 m

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