# Free fall question, where has my reasoning gone wrong?

DaveC426913
Gold Member
You show a speed vs time graph, yet the top and bottom of the elevator car are on different lines. (I think we can safely assume that they have the same speed!)

Draw a position vs time graph.
Right. Going back & forth between d/t and v/t graphs messed me up.

I couldn't do the d/t because PhotoShop doesn't plot a parabola very well.

hi, I solved it.. I just didn't know what they meant by "distance fallen relative to the elevator shaft". I was trying to find the position of the fallen bolt relative to the elevator shaft, but distance fallen is a different thing.

but distance fallen in units isn't relative to anything is it? if something falls x amount of km, it has fallen x amount of km's no matter how you look at it?

thanks

Doc Al
Mentor
hi, I solved it.. I just didn't know what they meant by "distance fallen relative to the elevator shaft". I was trying to find the position of the fallen bolt relative to the elevator shaft, but distance fallen is a different thing.
Finding the change in position of the bolt with respect to the elevator shaft will tell you the distance fallen with respect to the shaft.

but distance fallen in units isn't relative to anything is it? if something falls x amount of km, it has fallen x amount of km's no matter how you look at it?
No, the distance fallen very much depends on what you're measuring with respect to. For example, how far the bolt falls with respect to the elevator car is quite different than how far it falls with respect to the shaft.

but distance fallen in units isn't relative to anything is it? if something falls x amount of km, it has fallen x amount of km's no matter how you look at it?

thanks
I would say it does matter.

someone in the elevator will think it has fallen 9 feet. that's why they said "relative to
the elevator shaft"

No, the distance fallen very much depends on what you're measuring with respect to. For example, how far the bolt falls with respect to the elevator car is quite different than how far it falls with respect to the shaft.

Could you give me an example? if you say something like "the bolt fell 2 feet into the elevator" then how much will it have fallen from the perspective of the shaft? it would still be a fall of 2 feet wouldn't it?

Finding the change in position of the bolt with respect to the elevator shaft will tell you the distance fallen with respect to the shaft.
I'm not sure what it means entirely to say "change in position with respect to the elevator shaft" :S Does it mean to find the position of the bolt in the elevator shaft (so instead of 9 feet it would be like 25 feet or something), and then find the position of the bolt after 0.71 seconds and see the difference? This is what I thought before, but if it falls in 0.71 x amount of feet, then why would it make a difference if you were considering the bolt 9 feet in the air or 25 feet in the air?

Start by showing how you solved part a. What you should have done to solve it, is equate expressions for the position of the bolt and the floor of the elevator (with respect to the shaft or ground) as a function of time. You solve for the time when both are at the same place. Then just plug that time in to get the position.
yes I did that, but plugging in the time to get the position is the position in respect to the elevator right? Well, I did that and I took the difference between the elevators initial position and the new position, giving me the answer.. but now I'm confused because of what you guys are now saying

thanks

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Doc Al
Mentor
Could you give me an example? if you say something like "the bolt fell 2 feet into the elevator" then how much will it have fallen from the perspective of the shaft? it would still be a fall of 2 feet wouldn't it?
No. Here's a reverse example. Say you are in an elevator car and you drop a ball at the instant the cable breaks (and thus you are in free fall--forget about brakes or friction). Say you start out on the 100th floor and after some time you crash into the bottom of the shaft. During that fall, how far did the ball move with respect to the elevator car? Obviously you've fallen 100 floors with respect to the shaft.
I'm not sure what it means entirely to say "change in position with respect to the elevator shaft" :S Does it mean to find the position of the bolt in the elevator shaft (so instead of 9 feet it would be like 25 feet or something), and then find the position of the bolt after 0.71 seconds and see the difference?
Exactly.
This is what I thought before, but if it falls in 0.71 x amount of feet, then why would it make a difference if you were considering the bolt 9 feet in the air or 25 feet in the air?
It doesn't. All that matters is the change in position.

No. Here's a reverse example. Say you are in an elevator car and you drop a ball at the instant the cable breaks (and thus you are in free fall--forget about brakes or friction). Say you start out on the 100th floor and after some time you crash into the bottom of the shaft. During that fall, how far did the ball move with respect to the elevator car? Obviously you've fallen 100 floors with respect to the shaft.
oh okay, right. if you said something like x amount of feet from the elevator car or x amount of feet down the shaft, then it would be different.. then if you just measured the feet fallen without respect to anything what would you call that

Exactly.

It doesn't. All that matters is the change in position.
Okay, I'm not sure if I did it correctly, I found the amount of feet it fell from its initial position to its new position. I'm not sure how it's relative to the elevator shaft though.

thanks

Doc Al
Mentor
then if you just measured the feet fallen without respect to anything what would you call that
A meaningless number. Okay, I'm not sure if I did it correctly, I found the amount of feet it fell from its initial position to its new position. I'm not sure how it's relative to the elevator shaft though.
If you had an expression for the position of the bolt, it must have been with respect to something (even if you aren't quite sure to what). Show the expression that you used. (I'm sure it was with respect to the shaft/ground.)

A meaningless number. If you had an expression for the position of the bolt, it must have been with respect to something (even if you aren't quite sure to what). Show the expression that you used. (I'm sure it was with respect to the shaft/ground.)
first, for part a, I solved for the time by

9 + 8t -16t^2 = 8t + 2t^2

and then I got sqrt(9/18) which is 0.71 seconds.

then I plugged 0.71 into 9+8t - 16t^2 to see the new position it fell to.. then I took that position (6.680 feet) and subtracted it from the original 9 feet to get the distance fallen. I got 2.3 ft, but that led me the question about whether it mattered where I took the distance from and if it even mattered that I took the distance fallen from 9 feet in the air or 25 feet in the air - since I couldn't find the position of the bolt in the elevator shaft. but say, if I found out that the bolt was 15 feet in the air from the elevator shaft, the distance fallen from 9 to 6.680 would be the same as the distance fallen from 15 feet to 12.7 feet.

thanks

Doc Al
Mentor
first, for part a, I solved for the time by

9 + 8t -16t^2 = 8t + 2t^2
Good. Note that each side is the position with respect to the shaft. You don't know the actual height of the bolt or elevator floor, but all that matters is that the bolt starts off 9 ft higher than the elevator floor. Your equation just assumes that the elevator floor is at position y0 = 0, which is fine. (Who cares?)

Note that if you assumed that the elevator floor was initially at y0 = 25 ft and thus the bolt was at y0 = 25+9 = 34 ft, that nothing would change. The arbitrary 25ft would just drop out of the equation when you solved for the time or the change in position.

But all of your position measurements are with respect to the shaft.

Good. Note that each side is the position with respect to the shaft. You don't know the actual height of the bolt or elevator floor, but all that matters is that the bolt starts off 9 ft higher than the elevator floor. Your equation just assumes that the elevator floor is at position y0 = 0, which is fine. (Who cares?)

Note that if you assumed that the elevator floor was initially at y0 = 25 ft and thus the bolt was at y0 = 25+9 = 34 ft, that nothing would change. The arbitrary 25ft would just drop out of the equation when you solved for the time or the change in position.

But all of your position measurements are with respect to the shaft.
ah I see, thank you very much.

Just to clear something up though, wouldn't x0 = 9 and x1 = 0 be in respect to the elevator floor? Since I know that the bolt is 9 feet above the elevator floor, so 0 would be the elevator floor. On the other hand, in respect to the elevator shaft would be the distance of the bolt above the ground of the elevator shaft?

and how could I have measured it differently in terms of the elevator floor? I'm just not sure how the answer would've been different if I took it with respect to the elevator floor. I know that the position of the bolt after falling is in respect to the elevator floor, since the measurement of 9 feet is in respect to how high the bolt is above the elevator floor.

thanks

Doc Al
Mentor
Just to clear something up though, wouldn't x0 = 9 and x1 = 0 be in respect to the elevator floor?
It could be either with respect to the shaft or with respect to the elevator floor. The difference in initial position of bolt and elevator is the same from any reference. It's the subsequent position that changes depending on what you're measuring with respect to, not the initial position.

What tells me that you're measuring position with respect to the shaft are the expressions y = 9 +8t -16t^2 (for the bolt) and y = 8t + 2t^2 (for the elevator floor).

It could be either with respect to the shaft or with respect to the elevator floor. The difference in initial position of bolt and elevator is the same from any reference. It's the subsequent position that changes depending on what you're measuring with respect to, not the initial position.

What tells me that you're measuring position with respect to the shaft are the expressions y = 9 +8t -16t^2 (for the bolt) and y = 8t + 2t^2 (for the elevator floor).
ohh, I see, because my equation y= 8t + 2t^2 is the movement of position y from 0 along the elevator shaft. and likewise with my bolt equation, it starts 9 feet above the elevator floor and falls down in respect to the elevator shaft, so if I I picked some appropriate number, you could calculate how the bolt hits the ground of the elevator shaft with that equation. so the equation is really like y = a + 8t + 2t^2 and y = (a+9) + 8t -16y^2 .. Thanks :)

if you don't mind, could you show me an equation like this in respect to the elevator floor, so I can tell the difference in the future?

thanks

Doc Al
Mentor
if you don't mind, could you show me an equation like this in respect to the elevator floor, so I can tell the difference in the future?
To find the position of the bolt with respect to the elevator floor, just subtract the two expressions:
y = 9 -18t^2

Of course, the position of the elevator floor with respect to itself is just y = 0.

To find the position of the bolt with respect to the elevator floor, just subtract the two expressions:
y = 9 -18t^2

Of course, the position of the elevator floor with respect to itself is just y = 0.
Right, of course the new distance of the bolt in respect to the elevator floor is just 0, since it hits the floor :P

thanks a lot! I feel like I can tackle any kind of problem like this now :P