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

[steven1495]

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

 

[SHISHKABOB]

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

 

[steven1495]

Would a good equation for this be:
d=V₁Δt+ 1/2 at²

 

[azizlwl]

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.

 

[steven1495]

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

 

[azizlwl]

Maybe you sketch a velocity vs. time graph.
The area under the graph is the displacement.