How can I find the height and time of a freely falling object?

[whatsername]

If someone could please help me with the following question I would greatly appreciate it.

An object falls a distance h from rest. If it travels 0.5h in the last 1.00s, find the time and the height of its fall.

Ok, so for the second half that the object is falling, the velocity is 0.5h m/s, the time is 1.00s, the displacement is 0.5h m, and the acceleration is -9.8 m/s/s. For the first half, the acceleration is also -9.8 m/s/s, and the displacement is also 0.5h. The object is obviously going slower for the first half, so that velocity and time will be different. I'm not sure where to go from here so if anyone is willing to point me in the right direction that would be great. Thanks. :)

 

[hotvette]

I'm not sure where to go from here so if anyone is willing to point me in the right direction that would be great.

1. Draw a picture and label everything you know.

2. Write the equation of motion x = f(t) of the falling object.

3. Write, in relevant mathematical terms, other information you are given

- consider 2 moments in time, t1 which is when the object has fallen the first h/2 distance, and t2 which is when the object has fallen h distance.

- you should end up with equations relating x1 to t1, x2 to t2, and t1 to t2, which you can use to get the desired answer.

 

[whatsername]

Thanks for your reply. I am still pretty lost with this question though. I've tried using the different equations for constant acceleration and I can't seem to come up with anything that helps at all.

Is there a way for me to find the velocity of the first half of the object's flight? If I can find that then I can solve for time and add that to the 1.00s.

I've just started taking physics this year so unfortunately I'm not very experienced with this stuff.

Thanks for your help.

 

[hotvette]

Let me ask this. Can you tell me the equation of motion for a free falling object? y = f(t) Hint: there's a 1/2 in it, a g, and time is involved.

 

[whatsername]

I've been using y = y0 + v0t - 1/2 gt^2 which I'm pretty sure is right, but for the first half of the object's flight i don't know it's position or time so I'm not sure what I can do with it.

 

[hotvette]

That's the equation you need. Here are some things to consider:

- what is v0? Hint: the body starts from rest

- what is y0? Hint: did the body have an initial displacement at t=0?

- write the equation for y = h/2 (i.e. the first part) using time = t1 (i.e. you don't know the actual value)

- write the equation for y=h using time = t2 (i.e. you don't know the actual value)

- this gives you 2 equations with three unknowns (h, t1, t2)

- but, you are given t2-t1

Thus, you end up with 3 equations and 3 unkowns, which you can solve by substitution for h, t1, and t2.