Solving for Velocity of Falling Object with Air Resistance

In summary, the problem involves an object with a mass falling with a force equal to its own weight of 25 pounds. The air resistance also plays a role, causing a decelerating force that is equal to half of the object's velocity at any given time. The question asks for the velocity of the object after 8 seconds if it starts from rest. This can be solved using a free body diagram and Newton's laws, resulting in a differential equation. However, the wording of the problem is confusing and may contain errors.
  • #1
rlagustn
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An object with a mass if falling with a force that is equal to its own weight of 25 pounds. The air resistance causes a decelerate force equal to 1/2 the velocity of the object at any time. If the object falls from rest, what is the velocity of the object after 8 seconds?

I'm just confused at the wordings of the question. I just cannot find a way to start.
I tried to use to formula v(t) = (mg/b)t - (m^2*g / b^2) + m/b*vknot but the formula did not make sense to me. I was wondering if there are any other formulas I could use to solve this problem.
 
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  • #2
I'm just confused at the wordings of the question. I just cannot find a way to start.
Start with a free body diagram - draw all the forces on the object, the use Newton's laws.
You'll end up with a differential equation.
 
  • #3
rlagustn said:
An object with a mass if falling with a force that is equal to its own weight of 25 pounds. The air resistance causes a decelerate force equal to 1/2 the velocity of the object at any time. If the object falls from rest, what is the velocity of the object after 8 seconds?

I'm just confused at the wordings of the question. I just cannot find a way to start.
It is confusing. "Falling with a force" does not make much sense.
And a force equal to 1/2 the velocity it's definitely nonsense. The units do not match.
Is this the actual text of the problem?
 

Related to Solving for Velocity of Falling Object with Air Resistance

1. What is air resistance and how does it affect the velocity of a falling object?

Air resistance is the force that opposes the motion of an object as it moves through the air. It is caused by the friction between the air and the surface of the object. As an object falls, the force of air resistance increases, causing the object's velocity to decrease.

2. How do you calculate the velocity of a falling object with air resistance?

The velocity of a falling object with air resistance can be calculated using the equation v = gt - (m/k)(1 - e^(-kt)), where v is the velocity, g is the acceleration due to gravity, t is the time, m is the mass of the object, k is the drag coefficient, and e is the base of the natural logarithm.

3. What factors affect the velocity of a falling object with air resistance?

The velocity of a falling object with air resistance is affected by the object's mass, the drag coefficient of the object, the acceleration due to gravity, and the time it takes for the object to fall. Other factors such as air density and the shape of the object can also have an impact on the velocity.

4. How does the velocity of a falling object change as it reaches terminal velocity?

As an object falls, its velocity increases until it reaches a point where the force of air resistance is equal to the force of gravity. At this point, the object will no longer accelerate and will continue to fall at a constant velocity, known as terminal velocity.

5. Can air resistance ever completely cancel out the force of gravity on a falling object?

No, air resistance can never completely cancel out the force of gravity on a falling object. However, as the object's velocity increases, the force of air resistance will eventually become equal to the force of gravity, resulting in a constant velocity known as terminal velocity.

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