# Object Speed at Infinite Distance from Earth: 1660 m/s

• UrbanXrisis
In summary, the initial speed of the object is 2.00x10^4 m/s when fired from Earth's surface, and its speed when very far from Earth can be found by subtracting the escape velocity of Earth (11190.7 m/s) from the initial speed. However, the book states a different speed of 1660 m/s. To find the correct speed, one must consider the work done by Earth on the object and use the equation \Delta KE = \sum{Work} to find the final velocity when the object is very far from Earth. This can be done by finding the initial potential energy, which is zero at infinity.
UrbanXrisis
An object is fired from the Earth's surface with a speed of 2.00x10^4 m/s. What will its speed be when it is very far from the earth? (neglect friction)

so... what I did was find the excape velocity of the earth, which is 11190.7 m/s then subtract that from the initial speed.

my teacher said that when and object is fired at excape velocity, it will slow down to 0m/s when it is at an infinite distance from the earth. so if I just subtract 2.00x10^4-11190.7 then that will give me the velocity it should have, which is 8806 m/s, but my book says 1660 m/s. What did I do wrong?

The Gravitational Force can slow an object with an escape velocity to 0 at "infinity". Can you find out the work done by Earth when that object reach "infinity"?
Hint:
$$\Delta KE = \sum{Work}$$
Where
$$\Delta KE = -\frac{1}{2}mv^{2}_{esc}$$
So when an object is at "infinity", the Earth will do that amount of work on an object.
Use $\Delta KE = \sum{Work}$ again to find the final velocity when that object is very far from Earth.
Viet Dao,

Last edited:
Making the previous hint a bit more explicit. The work done is incorporated in the potential energy. The statement made by your teacher is equivalent to saying that escape velocity is the velocity needed to give the object a total energy (kinetic plus potential) of zero. By definition the potential energy is zero at infinity. That will let you figure out the initial potential energy in your problem

## 1. How is the object's speed determined at infinite distance from Earth?

The object's speed at infinite distance from Earth is determined using the equation v = √(GM/R), where v is the speed, G is the gravitational constant, M is the mass of Earth, and R is the distance from Earth's center.

## 2. Is the speed of the object constant at infinite distance from Earth?

Yes, the speed of the object remains constant at infinite distance from Earth as there are no external forces acting on it to change its velocity.

## 3. Can the object's speed at infinite distance from Earth be faster or slower?

No, the object's speed at infinite distance from Earth is constant and cannot be changed unless there is a change in the mass or distance of Earth.

## 4. How does the Earth's mass affect the object's speed at infinite distance?

The Earth's mass has a direct impact on the object's speed at infinite distance. The higher the Earth's mass, the faster the object's speed will be at infinite distance.

## 5. Is there a limit to how fast an object can travel at infinite distance from Earth?

Yes, there is a limit to how fast an object can travel at infinite distance from Earth. This limit is known as the escape velocity and is dependent on the mass and radius of the planet. For Earth, the escape velocity is approximately 11.2 km/s. Any object traveling faster than this speed will escape the planet's gravitational pull and continue on into space.

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