# Free fall body problem, stuck with 2 unknowns

1. Sep 10, 2007

### novice@physics

(moved to Intro Phys... - Doc Al)
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Hi guys,
this is my first post in this forum. I feel lucky to come across a place like this and even more thankful if i can get help on this problem that i've been spending a loooot of time on :(

Oh yea, I have virtually no background in physics (we mostly watched videos in high school) and i'm taking my first semester of physics in community college; it mainly deals with mechanics. so far in the 2 weeks that have passed, i have studied kinematics in one dimension and free fall body problems. i spent almost the whole day doing free fall body problems to gain insight and intuition on how to solve a problem but some of them are just too tough for me!

Well here's the problem.

Problem: "At t = 0, a stone is dropped from the top of a cliff above a lake. Another stone is thrown downward 1.6s later from the same point with an initial speed of 32 m/s. Both stones hit the water at the same instant. Find the height of the cliff."

My strategy was to solve for the first stone's position and velocity at t = 1.6s. (My reasoning is that at t = 1.6, the second stone is still at the origin being thrown.)

Since both stones hit the bottom at the same time, i assumed that the time elapsed from stone 1's fall at position y(t=1.6) to the bottom at y = h (i let displacement be positive downwards) will be the same time it takes for stone 2 to hit the bottom.

so then i let the displacement from stone 1 at t = 1.6s to the bottom equal (h - 12.557).

i then try to use a formula that will let me solve for time. that is going to be
deltaY = vnot(t) + (1/2)(a)(t)^2.

however, when i substitute in the values i know, i get stuck with two unknowns.

here's the paperwork that i have done so far (sorry if its messy, it's a rough draft that i will eventually transcribe neatly into the final hw paper that i will turn in):

i hope to get a decent handle on kinematics and free fall body problems because this week we're starting projectile motion and then a test covering all this the following week. arrrgh!!

thanks a million guys! :)

Last edited by a moderator: Sep 10, 2007
2. Sep 10, 2007

### olgranpappy

You should write down an equation for the first stone's position (unknown, call it 'y') as a function of time (involving only the known acceleration due to gravity and the time) and an equation for the second stone's position (unknown, call it 'y') as a function of time (involving only the known acceleration due to gravity and the known initial velocity and the time).

Solve both for time and set then equal to each other to find an equation for y in terms of only known quantities.

3. Sep 10, 2007

### Mentz114

If you can write 2 equations in 2 unknowns it is solvable. Using h for the height and t for the time taken for the first stone to hit the bottom we can write

h = 1/2gt^2 ( first stone)

h = 1/2g( t-1.6)^2 + 32.(t-1.6) ( second stone)

which might be correct.

4. Sep 10, 2007

### novice@physics

Thanks for the help guys!

I think another source of my problem was that I was trying to apply the same method that i used in an earlier but similar problem. So it is true then, that you can't master physics by rote. i read in a supplement help book that usually if there is a time delay in a free fall problem, you should try to solve the the first object at the time the second object has fallen. hmmm......

so then, do you just have to do a lot of problems to become proficient? like how can i build the intuition that you guys have?

thanks again. lots of help! :)

5. Sep 10, 2007

### PhanthomJay

Yes, you have to do a lot of problems to realize that the solution method noted above is the simplest, however, don't be discouraged because your method would work also, you just needed the second equation for the second stone (h =32t +1/2gt^2) to solve the problem. It required an extra step, but you'd get the same result, and your reasoning was very good. There is always usualy several ways to proceed, and only practice will give you the simplest or best way.

6. Sep 10, 2007

### Lateral

Practise doesn't make perfect, but it helps all the same. I find the best way to learn new physics and math ideas is to understand what's happening, label the known variables, realise what you need, and try find a formula that suites.

7. Jan 11, 2012

### yromelyn

t=1.6s
vi=32m/s
h=?
didn't you forget the aceleration due to gravity which is 9.8m/ssquared?

8. Jan 11, 2012

### Curious3141

I think there's a forum rule against "necroposting" - you're responding to a thread that's over 4 years old. I'll report the thread so it can be closed.