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(II) Take into account the Earth's rotational speed ( 1 rev/day)and determine the necessary speed, with respect to Earth, for arocket to escape if fired from the Earth at the equator in adirection $(a)$ eastward; $(b)$ westward; $(c)$ vertically upward.

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A) $10,700 \mathrm{m} / \mathrm{s}$B) $11,600 m / s$C) $11,200 \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

Rutgers, The State University of New Jersey

Hope College

McMaster University

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.

05:05

TThe earth rotates once pe…

03:04

The earth rotates on its a…

04:33

The earth rotates once per…

01:18

(a) Find the angular speed…

05:00

04:02

(II) What is the linear sp…

07:27

Earth revolves on its axis…

the speed of the surface of the earth. So we have the earth. This is directing from vest to East is basically given by we is equals Dubai the media's off the earth, divided by its time period riches equals to Dubai. 6.3 times turned to the par six divided by nearly 6400 seconds. If it is one revolution for day, it actually means about 4 86,400 seconds. If you saw that, you'll get 4 64 meters for a second Now this is the speed off the earth at the equator is relative to the center of the earth. We call it eastwards Velocity east borders plus X, we can say because the order is moving at this speed from west to east. So that is the velocity of any object on the surface of the earth traveling eastward. Basically, the escape velocity of the surface of the earth is given by square root off too g and e by our which is equals the square root of two times 6.67 times turned to the par negative 11 times the mass of the earth is 5.98 times 10 to the part of 24 on divided by 6.38 time. Stand to the far off. Six. If you sold that, you'll get the escape velocity is 1 11,082 mirror per second. Now the meaning of escape velocity is that an object has to be given this much velocity in order to escape the gravitational field of the earth from the surface of the Earth. And now what they're asking is that with the surface of the earth traveling Easter and in the first case, they're saying that if the rocket to escape from the earth is also fired eastward. So with the surface of the earth traveling east and the rocket's velocity to the east, the locket velocity and the Earth's velocity has to add up linearly to give this kid velocity. So I hope that it's clear, which means that we, the rocket relative to earth surface this velocity less 4 64 meters per second velocity has to actually give you the escape velocity muted per second. See if you saw that, then you will get the velocity of the rocket relative to Earth as approximately equals to 10,700 meters per second. That's the first part of the question. For the second part, they say that, um, the locket for a rocket to escape if the earth at the equator in a direction is vest word. So with the surface off the air, this traveling eastward earth is traveling, use toward and the rockets velocity is basically towards the best. Then we can say that v rocket relative do with the earth. If you are this velocity, do the earth velocity. Okay, then he should get velocity of 1 11,082 unit per second. So therefore you answer will be approximately 11,000 6 46 or 11,600 meters per second. So the surface of the traveling east and the rocket's velocity through the east in the first case, the locket velocity and the surface velocity, but early nearly. But for this part, with the surface of the traveling eastward and the locker this moving westward, the rocket velocity will have to be higher than the normal escape velocity. So therefore we get 11,600 meters per second on and see when fired vertically, upwards. So the rocket is fired vertically, upwards the locket velocity and the earth velocity on our right angles, the others velocity and the rockets velocity are dead right angles. So which means if you apply the right triangle a law of extradition. So we'll have B squared rocket relative to the earth less 4 64 squared that should be equals to 11,000 1 82 squared, which is escape velocity. So, in fact, the earth is traveling this side and the rocket is moving. The other words, basically for the personal stationery will see Knocker is moving in this direction. So that is the escape velocity. Should hae party needs is 11,000 wanted to? If you solve that, then you will get the rocket relative to the surface of the earth is equals to 1 11,072 which is approximately 11,200 meters per second. So that is the answer to the hard part here

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