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

## Homework Statement

It's a two part question, but it basically says this:

a bolt drops from an elevator 9.0 ft from the ground, at what time does it hit the ground?

## Homework Equations

x = x0 + vx0t + 1/2ax(t^2)

## The Attempt at a Solution

since it's a free fall question and we're starting from above ground:

0 = 9.0ft - 16ft/s^2 (t^2)

-9.0/-16 = t^2

t = 0.75 seconds.

But the book says that t = 0.71 seconds..

thanks

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Where does the 16ft/s^2 come from?

gravity is 32 ft/s^2 so 1/2ax(t^2) is -16ft/s^2(t^2)

Doc Al
Mentor

a bolt drops from an elevator 9.0 ft from the ground, at what time does it hit the ground?

so...

1 foot = 0.3048 m

so 9ft = 2.7432 m

(delta) y = Vot + 1/2(a)t^2

so 2.7432 = 0 + 1/2(-9.80)t^2

so 2.7432/(1/2*-9.8)=t^2

so .5598367347 = t^2

so t = .7482223832 or .75s

how come the answer says 0.71 seconds though? the equation sqrt(9/16) is not ambiguous, since they are both perfect squares.. I can't really guess that it was a difference due to rounding can I?

thanks

how come the answer says 0.71 seconds though? the equation sqrt(-9/-16) is not ambiguous, since they are both perfect squares.. I can't really guess that it was a difference due to rounding can I?

thanks
my math got me .75s (I stored the answers in my calculator so rounding error wouldn't be a factor)

DaveC426913
Gold Member
gravity is 32 ft/s^2 so 1/2ax(t^2) is -16ft/s^2(t^2)

Yeah. I realized as soon as I posted, so I deleted it so as not to confuse.

my math got me .75s (I stored the answers in my calculator so rounding error wouldn't be a factor)
that's what I got as well, you don't need a calculator to see that the sqrt( 9 / 16) is going to be 0.75.. but the problem is that the book says 0.71s, which is strange...

DaveC426913
Gold Member
What is the other part of this "two part question"? Is it possible that the 9.0 ft initial height was derived and thus possibly incorrect?

What is the other part of this two part question? Perhaps that factors in?
this is the full question:

An elevator ascends with an upward acceleration of 4.0ft/s^2. At the instant its upward speed is 8.0ft/s, a loose bolt drops from the ceiling of the elevator 9.0 ft from the floor.

Calculate (a) the time of flight of the bolt from the ceiling to the floor

(b) the distance it has fallen relative to the elevator shaft.

Answer: (a) 0.71 (b) 2.3 ft

I don't see how the other parts can affect the answer.. but there's a large chance that I'm wrong, I'm just learning physics myself through this book

thanks

What is the other part of this "two part question"? Is it possible that the 9.0 ft initial height was derived and thus possibly incorrect?
no, it is given

Doc Al
Mentor
this is the full question:

An elevator ascends with an upward acceleration of 4.0ft/s^2. At the instant its upward speed is 8.0ft/s, a loose bolt drops from the ceiling of the elevator 9.0 ft from the floor.

Calculate (a) the time of flight of the bolt from the ceiling to the floor
That's quite a bit different from the problem that you stated and solved! You can't ignore the acceleration of the elevator.

That's quite a bit different from the problem that you stated and solved! You can't ignore the acceleration of the elevator.
hmm, but that is the acceleration going up isn't it? when it falls, wouldn't the acceleration just be gravity?

thanks

DaveC426913
Gold Member
hmm, but that is the acceleration going up isn't it? when it falls, wouldn't the acceleration just be gravity?

thanks
Yes but it's initial velocity is not zero. And the elevator floor is moving.

This is not a two-part question. This is a one-part question that has several dependent components.

Doc Al
Mentor
hmm, but that is the acceleration going up isn't it? when it falls, wouldn't the acceleration just be gravity?
The acceleration of the bolt is just due to gravity. But you are asked for the time until it hits the moving floor, which is accelerating. You need to combine both accelerations. (Write the position of the bolt and the elevator--with respect to the ground--as functions of time. Then solve for the point at which they collide.)

ohh. I thought that they meant the floor of the elevator SHAFT. thanks.

I thought that a dropped object has an initial velocity of 0? If not, I'm not sure how I would calculate that.

Thanks for the replies

Doc Al
Mentor
ohh. I thought that they meant the floor of the elevator SHAFT. thanks.
D'oh! I thought that a dropped object has an initial velocity of 0? If not, I'm not sure how I would calculate that.
The dropped object will have the initial speed of whatever it's being dropped from. (In this case from a moving elevator.)

D'oh! The dropped object will have the initial speed of whatever it's being dropped from. (In this case from a moving elevator.)
A good way to think about this would be to think about what happens in a car. When you drop something out of the window, it keeps moving with the car's velocity, it doesn't start from rest. ;)

DaveC426913
Gold Member
I thought that a dropped object has an initial velocity of 0? If not, I'm not sure how I would calculate that.
Well your equation contains a variable for initial velocity. It's just not zero.

D'oh! The dropped object will have the initial speed of whatever it's being dropped from. (In this case from a moving elevator.)
Hi, but the speed of the elevator is going from the other direction? how does the upward speed transfer to a downward speed?
thanks

Doc Al
Mentor
Hi, but the speed of the elevator is going from the other direction? how does the upward speed transfer to a downward speed?
thanks
What do you mean? The initial speed of the bolt when it starts to fall from the elevator is the same as that of the elevator: 8 m/s upward. (After that, gravity exerts its influence, as for any projectile.)

What do you mean? The initial speed of the bolt when it starts to fall from the elevator is the same as that of the elevator: 8 m/s upward. (After that, gravity exerts its influence, as for any projectile.)

I'm not sure I fully understand... the bolt is DROPPED, so its orientation is opposite to the upward speed of the elevator? I would be certain if the elevator and the bolt were going in the same direction...

thanks

Doc Al
Mentor
I'm not sure I fully understand... the bolt is DROPPED, so its orientation is opposite to the upward speed of the elevator?
Why opposite? It's dropped--not thrown or pushed.

Think of the example with the car. You're in a car, riding along at constant velocity. You drop something. Does that something start moving in the opposite direction? No, its initial velocity is the same as that of the car.

Why opposite? It's dropped--not thrown or pushed.

Think of the example with the car. You're in a car, riding along at constant velocity. You drop something. Does that something start moving in the opposite direction? No, its initial velocity is the same as that of the car.

but being dropped is going down, so it's still opposite isn't it? since the elevator is going up

I can see your analogy but I'm having trouble accepting it (of course, that is entirely my fault). the claim seems to be "intuitive" but it isn't very intuitive to me..

when a speed is going in one direction, isn't there some kind of force that makes something go in that direction? if you drop something that isn't "going the same way", would it really have the same speed? perhaps I'm thinking of it like something going against the stream or a current?

sorry, but thanks for your patience

but being dropped is going down, so it's still opposite isn't it? since the elevator is going up

I can see your analogy but I'm having trouble accepting it (of course, that is entirely my fault). the claim seems to be "intuitive" but it isn't very intuitive to me..

when a speed is going in one direction, isn't there some kind of force that makes something go in that direction? if you drop something that isn't "going the same way", would it really have the same speed? perhaps I'm thinking of it like something going against the stream or a current?

sorry, but thanks for your patience
Yes, for as long as the bolt was part of the elevator, it was being accelerated by the same force that was accelerating the rest of the elevator.

When something is dropped, it just means that it is no longer traveling as part of whatever platform it was dropped off of.

The bolt, still connected to the elevator, was accelerated for some time to the velocity of the elevator. $$8 \tfrac{m}{s}$$

At that point, it broke off. What force, exactly, changed its velocity from $$8 \tfrac{m}{s}$$ to $$0 \tfrac{m}{s}$$?
That's right, none.

And according to Newton's First Law:
An object in motion tends to stay in motion, and an object at rest tends to stay at rest unless acted upon by an external force.

With no force to "remove" its initial velocity (Since it was traveling along with the elevator), the velocity of the bolt remains the same as it was the instant it detached from the elevator.
Just like how an object you drop out of the window of a moving car, has an initial velocity that's the same as that of the car the moment it was dropped.

Doc Al
Mentor
but being dropped is going down, so it's still opposite isn't it? since the elevator is going up
No. Being dropped just means "let go". Usually you drop things from rest, so they start going down immediately. But not necessarily.

Imagine you are shot straight up into the air out of a circus cannon holding a baseball. As you are going up, you let the ball go. (Ignore air resistance.) What happens to the ball?

when a speed is going in one direction, isn't there some kind of force that makes something go in that direction?
No, why do you think that? (Note that force is only needed to change motion, not to maintain motion.)
if you drop something that isn't "going the same way", would it really have the same speed?
How can it not be "going the same way"? You're holding it! Once you let go, of course, other forces take over. But initially it's moving with the same speed and direction as you are. How could it not?
perhaps I'm thinking of it like something going against the stream or a current?
Perhaps. But even then, if you are holding something and let it go it starts out moving at the same speed and direction that you are moving.