Calculating Distance Between a Window and a Roof in Freefall

  • Thread starter PhysWalk
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In summary, to find the distance between the top of the window and the roof of a building, we first use the equation d=vit+1/2at^2 to find the initial velocity at the top of the window, which is 5.143808511. Then, using the equation vf^2=vi^2+2ad, we can find the distance between the top of the window and the roof, which is 1.349937041 meters. It is important to remember to use the correct signs for acceleration and distance to avoid confusion.
  • #1
PhysWalk
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Homework Statement


The question is as follows: An object falls from the top of the roof of a building. The object falls past a 3.5 meter high window somewhere on the building ,in 0.47 seconds. Find the distance between the top of the window and the roof.

Homework Equations


V=d/t (Velocity = Distance over Time)
Vf^2=Vi^2 + 2ad (Velocity Final squared = Velocity initial squared + 2 times acceleration times distance)

I believe these are the equations that I should be using.

The Attempt at a Solution



3.5/0.47 = 7.44681 = V

So, Vf = 7.44681, Vi = 0 (assuming the object falls from rest), Acceleration = 9.8m/s/s, distance = X

7.44681^2 = 0^2 + 2 (9.8) (d)
55.455=19.6 (d)
55.455/19.6 = 2.82934
d = 2.82934
d = 2.8 meters.


And that is what I have so far, 2.8 meters from the top of the window, to the roof. Would this be the right approach to the problem? Or have I made a mistake?
 
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  • #2
The velocity you took is the average velocity for the fall past the window.
That's not what you need. You want to start by finding the velocity initail just as your object reaches the top of the window, you can do this using the position equation, but don't forget that it's still accelerating.
 
  • #3
the equation d=v*t tells you how far something has fallen in a time t while traveling at a velocity of v

Problem: The only time you have a constant velocity is when you're not accelerating. Something that's falling most definitely has an acceleration, which you presumably know since the problem is on earth

To approach this you want to start with the window part

It has a some Viw(Vi at start of window) you don't know, and some Vfw(velocity when it finishes passing the window) you don't know, but you DO know the time(.47 seconds)and you DO know the distance(3.5 meters) and the acceleration

You actually don't care about the Vfw, just the Viw, right(you can actually solve it with either but the problem asks for how far to the top of the window)? If you find Viw, we can zoom back out to the whole building and you know how fast it's going when it reaches the window now. So now you know Vi=0(the roof) and Vf=that speed you just found, Viw, and you still know a, so now you can find the associated distance to go from 0 to Viw
 
  • #4
Hi, and thanks for the replies, in response to blochwave, is this what you are talking about:

d=Vit+1/2at^2, so 3.5=Vi (0.47) + 1/2 (9.8) (0.47)^2 which = 5.143808511, and that is the Vi for the top of the window. So I can use that with:

Vf^2= Vi^2 + 2ad, so 5.143808511^2 = 0 + 2 (9.8) (d)

So, d= 1.349937041, I think
 
Last edited:
  • #5
If you didn't mess up one the calculator(I didn't check the actual numbers)it should be good

Remember that your acceleration is -g usually

It worked out ok because when you start from a higher place and fall to a lower place, d is negative(d=final position-initial!), so you forgot two negatives, which gave you velocity as a positive number, and so on

Well you effectively called the up direction negative and the down direction positive, which isn't BAD, in fact if you did it intentionally(don't lie!) it's probably good, but usually you just do the obvious and call down negative and up positive. It's easier that way when you have projectile motion that goes both up and down

We do usually feel safer working without negatives of course, but the danger is if you keep switching, using down as positive for falling motion, and down as negative for projectile, you're going to forget once, get some weird negatives, and drive yourself insane.

But if you don't forget you just look clever
 

Related to Calculating Distance Between a Window and a Roof in Freefall

1. What is acceleration?

Acceleration is the rate at which the velocity of an object changes over time. It is a vector quantity, meaning it has both magnitude and direction.

2. How is acceleration calculated?

Acceleration can be calculated by dividing the change in velocity by the change in time. The formula for acceleration is a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What causes acceleration?

Acceleration is caused by a net force acting on an object. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force and inversely proportional to its mass.

4. What is free fall?

Free fall is a type of motion where an object falls under the influence of gravity alone, without any other forces acting on it. In free fall, the only acceleration acting on the object is due to gravity, which is approximately 9.8 m/s² near the Earth's surface.

5. How does mass affect acceleration?

Mass and acceleration have an inverse relationship, meaning that as mass increases, acceleration decreases. This is because a larger mass requires a greater force to achieve the same acceleration as a smaller mass.

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