Distance travelled of an object falling from non-negligible height

In summary, the conversation discusses the limitations of using 9.8 m/s^2 as the acceleration due to gravity in a free-fall problem, particularly when falling from a significant height. The conversation then delves into the use of calculus to derive an equation for the distance fallen as a function of time and initial height. The equation involves using the mass and distance of an object in relation to a planet, and constructing a v-t graph to determine displacement. It is suggested that further knowledge of calculus is necessary to fully understand this type of physics problem.
  • #1
kaikalii
17
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In a free-fall problem, 9.8 m/s^2 works fine as long as you stay close to the earth. However, if you are falling from very high up, the change in acceleration due to gravity is no longer negligible.

Let's say there's an atmosphereless planet of mass M, and another object of negligible mass is falling toward it after being dropped from a point a distance r from the center of the planet. How could you derive an equation to find the distance fallen d as a function of time t and initial height r? Just so you are aware, I have a very limited knowledge of calculus (how to find derivatives and integrals), so please answer in terms I can understand.
 
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  • #2
You will need to learn more calculus in order to understand this sort of physics.
If you just do F=ma as usual you get:
$$\frac{GM}{r^2(t)} = \frac{d^2}{dt^2}r(t)$$

Basically you construct a v-t graph - which will be a curve.
The area under it is the displacement.
 
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1. What is the formula for calculating the distance travelled of an object falling from non-negligible height?

The formula for calculating the distance travelled of an object falling from non-negligible height is d = 1/2 * g * t^2, where d is the distance travelled, g is the acceleration due to gravity (9.8 m/s^2), and t is the time the object has been falling.

2. How does air resistance affect the distance travelled of an object falling from non-negligible height?

As an object falls, it will experience air resistance which opposes its motion. This will result in a decrease in acceleration and therefore a decrease in the distance travelled. The exact amount of air resistance will depend on the size, shape, and density of the object.

3. Does the mass of the object affect the distance travelled when falling from non-negligible height?

According to the formula for calculating the distance travelled, mass does not affect the distance an object will fall. However, in reality, objects with larger mass will experience more air resistance and therefore may not fall as far as lighter objects.

4. How does the height from which the object is dropped affect the distance travelled when falling from non-negligible height?

The height from which an object is dropped will affect the distance travelled. The higher the starting height, the longer the object will have to accelerate and therefore the farther it will fall. However, as the object reaches terminal velocity, the distance travelled will not continue to increase significantly.

5. Is there a limit to the distance an object can fall from non-negligible height?

Technically, there is no limit to the distance an object can fall from non-negligible height. However, as the object falls, it will eventually reach terminal velocity and will no longer accelerate. This means that there is a limit to how far an object can fall before it reaches a constant velocity.

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