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Chapter 1: Q40E (page 61)

A lunar lander is makingits descent to Moon Base I (Fig. E2.40). The lander descendsslowly under the retro-thrust of its descent engine. The engine iscut off when the lander is 5.0 m above the surface and has a downwardspeed of 0.8m/s . With the engine off, the lander is in freefall. What is the speed of the lander just before it touches the surface?The acceleration due to gravity on the moon is 1.6m/s2.

Short Answer

Expert verified

The speed of the lander just before it touchesthe surface is v=08m/slocalid="1655200617790" v=4.08m/s.

Step by step solution

01

Given data 

Distance from which lander experiences free fall due to gravity is h=5.0m

The downward speed of the lander is u=0.8m/s

The acceleration due to gravity at the moon is a=1.6m/s2a=1.6m/s2

02

Solution

Newton’s third law of motion can be expressed as,

v2=u2+2ah

Where is the final velocity which is before touching the ground

Substituting these values in the above expression gives,

v2=0.8m/s2+21.6m/s2×5.0mv2=4.08m/s2v=4.08m/s

Thus, the final velocity of the lunar lander before touching the surface is v=4.08m/s

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