Solve a Challenging Kinematics Question: Depth of a Shaft after 6.2 seconds

[Intr3pid]

I was wondering how u solve this kinematics question:

a banana peel is dropped from rest down a shaft. 6.2 s later the sound of the banana hitting the ground is heard. how deep is the shaft


i think:

v1= 0m/s
a=9.8m/s^2

i'm reallu stuck on this one.. don't know where to go from here.

 

[Diane_]

You also know the time. What you need is a relationship between acceleration, initial velocity, time and distance. Can you think of one?

 

[Intr3pid]

You also know the time. What you need is a relationship between acceleration, initial velocity, time and distance. Can you think of one?

is this the relationship?

d=v1t+ 1/2 at^2?

 

[Diane_]

That's the one. Note that one term drops out completely, and you have a relatively easy solution.

 

[Intr3pid]

That's the one. Note that one term drops out completely, and you have a relatively easy solution.

so I'm guessing v1t drops out since v1 = 0m/s. so i just use plug into d=1/at^2 to solve?

 

[Diane_]

That would do it.

 

[sweetrose]

I'm just wondering if the problem gave you any other information, because you stated this was a really hard kinematics question.

When we were working on kinematics, we worked on a similar problem, but the problem also stated the speed of sound...

If not, then it seems like a relatively easy problem to solve once you write down all the variables and choose the right kinematics equation to use.

 

[mukundpa]

The depth calculated will not that small that the time taken by the sound to come up can be ignored. Particularly when time is 6.2 sec.

 

[HallsofIvy]

There are two parts to this problem. First, assuming some depth, d, find the time it would take the banana peel to hit the bottom (in terms of d, of course). Second, using the speed of sound, find the time for the sound to go from the bottom back up (again, in terms of d). The sum of those two times is 6.2 s. Solve that equation for d.

I am, however, bothered by the choice of "banana peel". Not only would I expect air resistance to be important for a falling banana peel, I would be surprized if you could hear one hitting the bottom at all!