Chapter 14, Problem 35A

What is the maximum possible speed of impact upon Earth’s surface for a faraway object initially at rest that falls to Earth due only to Earth’s gravity?

To determine

The maximum possible speed of impact upon Earth’s surface for a faraway object.

Answer to Problem 35A

Equal to escape velocity $11.2km/s$ .

Explanation of Solution

Introduction: Escape velocity is the minimum speed needed by an object to escape permanently from the gravitational pull that holds it.

When an object at rest acquires the speed equals to escape velocity, its escape from the gravitational pull that holds it inside. Similarly, an object at rest outside the gravitational field, when falls in the Earth’s gravity, it will achieve the same speed at which it goes out. That is, it will impact the same escape velocity upon the surface of Earth due to Earth’s gravity.

Conclusion: Thus, without any external force, Earth’s gravity will attract the object just inside the gravitational field and falls upon the surface with the same $11.2km/s$ .