Free fall question, where has my reasoning gone wrong?

[emyt]

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]

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).

 

[emyt]

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]

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.

 

[emyt]

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