Explanation:
We start by using the conservation law of energy:
or
Simplifying the above equation, we get
We can rewrite this as
Note that the expression inside the parenthesis is simply the acceleration due to gravity so we can write
where is the launch velocity.
Answer:
The magnitude of the gravitational field strength near Earth's surface is represented by approximately .
Explanation:
Let be M and m the masses of the planet and a person standing on the surface of the planet, so that M >> m. The attraction force between the planet and the person is represented by the Newton's Law of Gravitation:
Where:
- Mass of the planet Earth, measured in kilograms.
- Mass of the person, measured in kilograms.
- Radius of the Earth, measured in meters.
- Gravitational constant, measured in
.
But also, the magnitude of the gravitational field is given by the definition of weight, that is:
Where:
- Mass of the person, measured in kilograms.
- Gravity constant, measured in meters per square second.
After comparing this expression with the first one, the following equivalence is found:
Given that ,
and
, the magnitude of the gravitational field near Earth's surface is:
The magnitude of the gravitational field strength near Earth's surface is represented by approximately .