Question

A lunar lander is making its descent to Moon Base I. Thelander descends slowly under the retro-thrust of its descentengine. The engine is cut off when the lander is 5.0{\rm m} above the surface and has a downward speedof 0.80 {\rm m/s} . With the engine off, the lander is in freefall.

What is the speed of the lander just before it touches thesurface? The acceleration due to gravity on the moon is 1.6\;{\rm m}/{\rm s}^{2}

Answer 1

`v_(f)=4.08m/s`

Step-by-step explanation:

Given data

Let the +y direction downwards

Δy (vertical displacement of the lander)=5 m

vi (initial velocity of lander)=0.8 m/s

a (acceleration due to gravity)=1.6 m/s²

To find

Final Speed vf of lander

Solution

To find final velocity use below equation

So

vf²=vi²+2aΔy

Substitute the given values to find final velocity

`(v_(f)) ^(2)=(0.8m/s)^(2)+2(1.6m/s^(2) )(5m)\\ v_(f)=\sqrt{(0.8m/s)^(2)+2(1.6m/s^(2) )(5m)}\\ v_(f)=4.08m/s`