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The Lunar Module could make a safe landing if its vertical velocity at impact is 3.0 $\mathrm{m} / \mathrm{s}$ or less. 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 is $(a)$ zero; $(b) 2.0 \mathrm{m} / \mathrm{s}$ downward; $(c) 2.0 \mathrm{m} / \mathrm{s}$ upward. Use conservation of energy to determine $h$ ineach case. The acceleration due to gravity at the surface of the Moon is 1.62 $\mathrm{m} / \mathrm{s}^{2}$ .

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A) 2.8$m$B) 1.5$m$C) 1.5 $\mathrm{m}$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

University of Washington

Hope College

University of Sheffield

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

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The Lunar Module could mak…

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(II) The Lunar Module coul…

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there was an example but t…

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04:24

A lunar lander is descendi…

00:56

In the final stages of a m…

03:47

02:41

The 15200 -kg lunar lander…

01:12

Touchdown on the Moon. A l…

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Let's investigate a p…

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A $1.14 \times 10^{4} \mat…

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A $1.14 \times 10^{4}$ -kg…

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A lunar lander is making i…

So the fashion about the lunar landing here and in this problem we have the lunar model. Okay, so this is the lunar module and it's supposed to land on the surface of the bone and it can actually land on the surface if its velocity is three meters per second or less. So we want to find out where the greatest height and vista pilot this height and rich you're shut off the engine that it can land safely under those conditions. So we'll have the substance. One was reference to the location range and is shut off and do the location. The surface of the moon and upward direction is positive and we're gonna ply conservation of energy. So we have even as equals zero dislocation we have I want as equals to EJ and a dislocation to land safely. Your velocity should be three meters per second and the height is you know, so are these two locations will have even is equals to Tito. So again we have half em even squared. Bless Emma. Gee, why one should be equals to have him we to squired class m g y two. The total energy of these two locations should be the same. So we have MG edge because this velocity zero equals on the right inside half M V two squared because y two is, you know, here. So if you saw that he will get urges equals to be two squired by two g and that should give you a 2.8 meters. The pilots were shut off the engine for it to see if safely put a line safely at three meters per second. All right, for the be part of the problem we need to find with same conditions except behalf of even is negative two meters per second. So now again, we'll write even is equals to eat too. And we have half m v even squared less mg by one is equals 2/2 em Vito's quiet place MG Y two. So have I. And villains squared. Bless Ama ji by one should be equals. Do you have him, Vito squared? Because this is the landing. Why too? And the velocity and this location known is not zero, but it is negative two meters per second. So if you saw that you will get EJ is equals to be two squad minus V even squared, divided by to a gene arranging the equations so you'll get three minus minus two squared, divided by two times 1.62 is the value of G on the surface, that should give you 1.5 meters. So that is the answer to the be part. And for the sea part we have the same conditions. Except now vivant is too meters per second. So we'll use the same equations. In this case, we'll have half em even squared, less mg why one is equals to have m v two squared. So again we get the same thing. V two squared minus. We even squared by two g. We get three minus minus. Do squared divided by two times 1.62 Sorry is this positive Should give you 1.5 meters. So in this case, also the answer is 1.5 meters

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