Speed of falling object via derivation/integration

In summary, the conversation discusses the process of determining the speed at which a stone strikes the ground when dropped from a certain height. The equation v=sqrt(2gh) is used, with the understanding that no air resistance is present. Two approaches are suggested - using kinematics/energy or integrating the equation ma=mg with respect to time. The final conclusion is that the speed can be determined through either method.
  • #1
warfreak131
188
0

Homework Statement



A stone is dropped from rest at an initial height h above the surface of the earth. Show that the speed with which it strikes the ground is v=sqrt(2gh)

Homework Equations





The Attempt at a Solution



I'm just not sure where to get started. I fully understand how to integrate/derive. I am having trouble understanding what equations to start with.

EDIT: I assume that I have to derive/integrate somewhere. I understand how to get sqrt(2gh) just by re-arranging the equation vf2 = vi2+2gh
 
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  • #2
Assuming no air resistance, then the resultant force acting on the mass m is ma=mg.

You can write 'a' as 'dv/dt' and integrate.

Though using kinematics/energy is much simpler.
 
  • #3
rock.freak667 said:
Assuming no air resistance, then the resultant force acting on the mass m is ma=mg.

You can write 'a' as 'dv/dt' and integrate.

Though using kinematics/energy is much simpler.

that would give me dv/dt = g. if i integrate with respect to t, id get v=gt

edit: nevermind, i got it,thanks
 

FAQ: Speed of falling object via derivation/integration

1. What is the formula for calculating the speed of a falling object?

The formula for calculating the speed of a falling object is v = gt, where v is the final velocity, g is the acceleration due to gravity (9.8 m/s²), and t is the time the object has been falling.

2. How does the speed of a falling object change over time?

The speed of a falling object increases at a constant rate of 9.8 m/s² due to the acceleration of gravity. This means that every second, the object's speed increases by 9.8 meters per second.

3. How can the speed of a falling object be determined using calculus?

The speed of a falling object can be determined by taking the derivative of the position function with respect to time. This will give the instantaneous velocity of the object at any given time.

4. What is the relationship between the position, velocity, and acceleration of a falling object?

The position of a falling object is dependent on its velocity, which in turn is dependent on its acceleration. The position of the object can be calculated by integrating the velocity function over time, and the velocity can be calculated by taking the derivative of the position function.

5. How does air resistance affect the speed of a falling object?

Air resistance can slow down the speed of a falling object by creating an opposing force to the object's motion. This means that the object will not accelerate at a constant rate of 9.8 m/s² and will reach a maximum velocity known as the terminal velocity, where the air resistance force is equal to the force of gravity.

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