Another! brain teaser.

[achris]

This one shouldn't be too hard...

Two bowling lanes, exactly the same characteristics. Two bowling balls, also with exactly the same characteristics.. The only difference is that half way down the lanes one of them has a gentle slope down, for another quarter of the lane, then comes back up to the original level and the other lane slopes up at the halfway point for another quarter and then slopes back down to the original level... The two balls are released onto the lanes at exactly the same time and at exactly the same speed.... The balls run down the lanes and remain in contact with the lanes at all times. Three possible outcomes... the balls arrive at the other end at the same time, or one or other is first....

Which is it?

Chris................
(I'll be offshore until 20th, so you have until then to work it out )

This is an ascii drawing that will attempt to represent what's been described.

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[Bass Man Bruce]

Re: Another! brain teaser.

They arrive at the same time, but the poser of the question doesn't care as he is fishing.

 

[JB]

Re: Another! brain teaser.

What Bruce said.

 

[blouderback]

Re: Another! brain teaser.

Too easy. They arrive at the same time, because they both have to climb the hill, and they both have to go down the hill. Doesn't matter what order they climb or go down. Right?

 

[SpinnerBait_Nut]

Re: Another! brain teaser.

What they said^^^^^

 

[arboldt]

Re: Another! brain teaser.

Actually, I think the one with the downhill slope first would arrive slightly ahead.

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Here's why. Both are launched at the same velocity. When the first one hits the downhill slope, it accelerates, then continues at the faster speed on the (lower) level. When it encounters the uphill slope, it will lose some kinetic energy to approximately its original speed.

The second ball would slow down when it hits the uphill section, and continue at the slower speed on its (upper) level. When it eoncounters the downhill slope, it accelerates to approximately its original speed.

Although they would finish at approximately the same speed, for the middle sections they would be traveling at slightly different speeds.

There are several assumptions -- 1) ignore effects of friction. 2) uphill and downhill sections are sloped enough that rolling will allow increase / decrease in kinetic energy (i.e. a sudden drop would transmit that additional acceleration in the direction of movement [straight down] instead of lateral).
3) You'd have to have insturments sensitive enough to actually detect the differences.

 

[BoatBuoy]

Re: Another! brain teaser.

arbodlt's assesment makes sense. I'll vote for him.

 

[angus63]

Re: Another! brain teaser.

Example of what Arboldt has deduced:


Lanes 100ft 50 ft flat 25 ft transition 25 ft flat
Balls initial velocity 5 ft/sec
Transition causes 1ft/sec acceleration/decelleration

Ball 1:
50 ft flat@ 5ft/sec--- 10 sec
transition (+1ft/sec)-- 6ft/sec for 25 ft = `4.167 sec
25 ft flat@ 5ft/sec --- 5 sec
Total time = 19.167 sec

Ball 2
50 ft flat @ 5 ft/sec -- 10 sec
25 ft transition (-1ft/sec)--- 4 ft/sec for 25 ft = 6.25 sec
25 ft flat @ 5ft/sec ---- 5 sec
Total time = 21.25 sec

I'm with you sir!!!!

 

[achris]

Re: Another! brain teaser.

They arrive at the same time, but the poser of the question doesn't care as he is fishing.

Wrong on both counts... Sadly I am working...

 

[achris]

Re: Another! brain teaser.

Actually, I think the one with the downhill slope first would arrive slightly ahead.....

Correct!!! Well done and with a perfect explanation too....

Chris............

 

[SgtMaj]

Re: Another! brain teaser.

Since this has already been answered with the real answer... I'll just stick to the silly answers...

The one that had the valley hit no pins because his was a gutterball.

Yeah, that's about all I've got right now. Sad, isn't it?

 

[oops!]

Re: Another! brain teaser.

awwww man i missed this, cause the time change....

but i got it right.......

what ya doin offshore chris....? diving?....or diving with a spear gun in yer hand? ...hee hee

 

[lakelivin]

Re: Another! brain teaser.

achris's description of the lanes doesn't match his sketch (or at least the description is ambiguous). As described, I picture a lane that's level for 1/2 it's length, slopes gently down for 1/4 length, and then slopes back up for the last 1/4 length, reaching the original starting level at the pins (and vice versa for the other lane). I.e., neither lane is level after the 1/2 point; it is either sloping down for 1/4 lane or sloping up for 1/4 lane.

In that scenario, does one ball arrive before the other?

 

[achris]

Re: Another! brain teaser.

achris's description of the lanes doesn't match his sketch (or at least the description is ambiguous). As described, I picture a lane that's level for 1/2 it's length, slopes gently down for 1/4 length, and then slopes back up for the last 1/4 length, reaching the original starting level at the pins (and vice versa for the other lane). I.e., neither lane is level after the 1/2 point; it is either sloping down for 1/4 lane or sloping up for 1/4 lane.

In that scenario, does one ball arrive before the other?

Yes, and for the same reasons as stated earlier...

oops... I'm an ROV pilot... Underwater robots basically... We have been running pigging operations and are just about to go out and replace a water intake grill on a rig... I'm currently in a hotel for a couple of days for a change from sleeping on the vessel.... Boat sails on Sunday afternoon...

 

[i386]

Re: Another! brain teaser.

Example of what Arboldt has deduced:


Lanes 100ft 50 ft flat 25 ft transition 25 ft flat
Balls initial velocity 5 ft/sec
Transition causes 1ft/sec acceleration/decelleration

Ball 1:
50 ft flat@ 5ft/sec--- 10 sec
transition (+1ft/sec)-- 6ft/sec for 25 ft = `4.167 sec
25 ft flat@ 5ft/sec --- 5 sec
Total time = 19.167 sec

Ball 2
50 ft flat @ 5 ft/sec -- 10 sec
25 ft transition (-1ft/sec)--- 4 ft/sec for 25 ft = 6.25 sec
25 ft flat @ 5ft/sec ---- 5 sec
Total time = 21.25 sec

I'm with you sir!!!!

Your example does not match the drawing. There are 2 transitions on each lane. In your example, there are only one per lane.

According to the drawing:

[Ball 1]
Begin motion: Ball rolls at constant speed on level surface
Transition 1: Acceleration down inclined plane
Constant Speed on level surface
Transition 2: Deceleration up inclined plane
Constant Speed to end of lane

[Ball 2]
Begin motion: Ball rolls at constant speed on level surface
Transition 1: Deceleration up inclined plane
Constant Speed on level surface
Transition 2: Acceleration down inclined plane
Constant Speed to end of lane

I think the second transition will negate the first.



I agree with what angus63 presented. I just don't agree that it matches the problem given.

 

[angus63]

Re: Another! brain teaser.

Your example does not match the drawing. There are 2 transitions on each lane. In your example, there are only one per lane.

According to the drawing:

[Ball 1]
Begin motion: Ball rolls at constant speed on level surface
Transition 1: Acceleration down inclined plane
Constant Speed on level surface
Transition 2: Deceleration up inclined plane
Constant Speed to end of lane

[Ball 2]
Begin motion: Ball rolls at constant speed on level surface
Transition 1: Deceleration up inclined plane
Constant Speed on level surface
Transition 2: Acceleration down inclined plane
Constant Speed to end of lane

I think the second transition will negate the first.



I agree with what angus63 presented. I just don't agree that it matches the problem given.

Look closer

each ball starts at 5ft/sec acelerates or decellerates and then returns to 5ft/sec

Both balls change speed twice 5 to 6 to 5 --- 5 to 4 to 5 in my example


Hope that helps