Free Fall Object: Time and Height Calculations from Rest | Homework Equations

In summary, an object in free fall can be solved using the one-dimensional constant acceleration equations, regardless of its mass. The distance traveled in the last second of free fall can be used to find the total time and height of the fall. The equation d=V1Δt+ 1/2 at2 can be used to calculate the distance with known acceleration, initial velocity, and time. Sketching a velocity vs. time graph can help visualize the problem and calculate the displacement.
  • #1
steven1495
20
0

Homework Statement



If an object travels half its total path in the last second of its free fall, from rest, find:
(a) the time, and
(b) the height of the fall


Homework Equations



I'm not sure at all what equations to use

The Attempt at a Solution



The only thing I can think of is just assuming a mass of an object, and guessing the time, but I didn't have any luck with this
 
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  • #2
an object in free fall is just a one-dimensional constant acceleration problem with an acceleration of -9.8 m/s2

If you recall your equations of one-dimensional constant acceleration, you should remember that mass does not play a role. At least in a simplified problem like this one.

If the object falls half its total distance traveled in the last second, that means that it also fell the first half of its distance in a time equal to the total time minus one second
 
  • #3
Would a good equation for this be:
d=V1Δt+ 1/2 at2
 
  • #4
steven1495 said:
Would a good equation for this be:
d=V1Δt+ 1/2 at2

Yes, that's equation for constant acceleration.
For easier calculation, assign acceleration as positive.

Write down all the known data and the unknown data.
If there are 3 unknown data, then you have to find 3 independent equations.
 
  • #5
the known data is
a= -9.800 m/s^2
Vi= 0 m/s

I used the above equation to find the distances with the times, but all the times I did (up to 6 seconds) didn't work, because after 6 seconds, the distance for the last second was less than the sum of all the other distances
 
  • #6
Maybe you sketch a velocity vs. time graph.
The area under the graph is the displacement.
 

1. What is free fall?

Free fall refers to the motion of an object falling under the influence of gravity alone, with no other forces acting on it. In this type of motion, the object experiences constant acceleration due to gravity and its velocity increases as it falls.

2. How is time calculated for a free fall object?

The time taken for a free fall object to reach a certain height can be calculated using the equation t = √(2h/g), where t is the time in seconds, h is the height in meters, and g is the acceleration due to gravity (9.8 m/s²).

3. How do you calculate the height of a free fall object at a certain time?

The height of a free fall object at a certain time can be calculated using the equation h = ½gt², where h is the height in meters, g is the acceleration due to gravity (9.8 m/s²), and t is the time in seconds.

4. What is the difference between time and height in free fall?

Time and height are two different variables used to describe the motion of a free fall object. Time refers to the duration of the fall, while height refers to the vertical distance traveled by the object during the fall.

5. Can the equations for free fall be used for objects with air resistance?

No, the equations for free fall assume that there is no air resistance acting on the object. In real-world situations, air resistance can significantly affect the motion of a falling object, and more complex equations are needed to accurately calculate its time and height.

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