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 3.0 m/s or less. The acceleration due to gravity at the surface of the Moon is 1.62 m/s2.

a) Suppose that you want to determine the greatest height h1 at which the pilot could shut off the engine if the velocity of the lander relative to the surface is zero. Use conservation of energy to determine h1.
Express your answer to two significant figures and include the appropriate units.

b)

Suppose that you want to determine the greatest height h2 at which the pilot could shut off the engine if the velocity of the lander relative to the surface is 1.8 m/s downward. Use conservation of energy to determine h2.

Express your answer to two significant figures and include the appropriate units.

c)

Suppose that you want to determine the greatest height h3 at which the pilot could shut off the engine if the velocity of the lander relative to the surface is 1.8 m/s upward. Use conservation of energy to determine h3.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

a) as we know

v^2= u^2+2 aS

3*3= 0+ 2* 1.62* s

s= 2.78 m/s

b) v^2= u^2+ 2 aS

3*3= 1.8*1.8+2*1.62* s

s= 1.78 m

c) 3*3= (-1.8)^2+2 *1.62*S

s= 1.78 m

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