[Guest]

I designed a mini submarine and wanted to test out the crush depth. I will place the unmanned sub on auto decent and wait for the crushed subs released air bubbles at the surface. I only have a stop watch and no other instruments. I know my sub descends at 18 Fps and the air bubbles rise at 4 Fps. After 9 minutes and 10 seconds the bubbles arrive right on time much to my excitement.

What was my designed crush depth for the mini submarine?

[Guest]

It crushes at a depth of 1800 ft after 100 seconds. It takes the airbubble the remaining 450 seconds to return to the surface.

[Guest]

It crushes at a depth of 1800 ft after 100 seconds. It takes the airbubble the remaining 450 seconds to return to the surface.

he said - crushed at 1800 F (is that fathoms or feet?) - but in a spoiler.

Hopefully that was also the 'designed' crush depth.

[Guest]

The complete solution:

First off we convert 9min 10sec to seconds, 550seconds total.

We know that the distance submerged by the sub is equivalent to the distance the bubbles must rise. Therefor, 18t=4(550-t) where t is the time taken to sumberge.

Solving for t we get t=100 seconds which agrees with Raschaller.

We can now find the depth at which the sub was crushed by multiplying the time it took to go down with the rate, 18fps*100sec, which gives 1800feet/fathoms (whatever units are being used).

[Guest]

I couldn't derive the correct formula, so I had to use trial and error. Thanks

The complete solution:

First off we convert 9min 10sec to seconds, 550seconds total.

We know that the distance submerged by the sub is equivalent to the distance the bubbles must rise. Therefor, 18t=4(550-t) where t is the time taken to sumberge.

Solving for t we get t=100 seconds which agrees with Raschaller.

We can now find the depth at which the sub was crushed by multiplying the time it took to go down with the rate, 18fps*100sec, which gives 1800feet/fathoms (whatever units are being used).

[Guest]

Good job, I wondered if I could have left out any information.

[Guest]

I designed a mini submarine and wanted to test out the crush depth. I will place the unmanned sub on auto decent and wait for the crushed subs released air bubbles at the surface. I only have a stop watch and no other instruments. I know my sub descends at 18 Fps and the air bubbles rise at 4 Fps. After 9 minutes and 10 seconds the bubbles arrive right on time much to my excitement.

What was my designed crush depth for the mini submarine?

I am wondering if we need to consider that when the air bubbles are first released they too are traveling downward at 18 fps. Would they not have to decelerate to zero, change direction and then accelerate to 4 fps?

[Guest]

I was going to put in a line about the bubbles instantly rise and are not moving downward, but I forgot.

[Guest]

I am wondering if we need to consider that when the air bubbles are first released they too are traveling downward at 18 fps. Would they not have to decelerate to zero, change direction and then accelerate to 4 fps?

Not enough information is given to determine the acceleration to the terminal velocity of 4 fps for the bubbles. The OP also doesnt state the reference point for the velocity of the bubbles so it should be assumed to be the same as the point for the submarine which is the sea floor, or some other stantionary boundary.