The Lunar Lander In Verne\'s book the astronauts did not land on the moon, but i

Question

The Lunar Lander In Verne's book the astronauts did not land on the moon, but in 1969 a lunar lander from the Apollo 11 mission did. To avoid a crash landing, the lander was equipped with landing probe which extended 5 feet (1 ft = 0.3048 m) below the landing gear. The idea was to descend very slowly RADAR ANTENNA until the probe touched the surface, at which point the engine would be switched off and the lander would fall to the surface. Assume that the downward velocity of the lander was 0.1 m/s at the time the probe touched the surface. How long did it take for the lander to reach the surface after the engine was shut off? The acceleration due to the moon's gravity is 1.62 m/s^2. How long would it have taken on Earth?

Explanation / Answer

a) h =ut + 1/2 at^2

h = 5ft = 1,524 m

1.524 = 0.1 t + 0.5 (1.62)t^2

0.81 t^2 + 0.1 t - 1.524=0

t = - 0.1+- sqroot (0.01 + 4 x 0.81 x 1.524 )/ 2 (0.81) = 1.311 seconds aprx

b) for earth,

1.524 = 0.1 t + 0.5 (9.8)t^2

4.9t^2 +0.1 t - 1.524 = 0

t = -0;1 +- sqroot ( 0.1^2 + 4 x 4.9 x 1.524)/ 2( 4.9) = 0.547 seconds apprx

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