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Comment by AlecBG | Hacker News Reader

First one water is lower. Ball is more dense than water, in boat displaces its weight in water, in water displaces it's volume

Dip for hill roll is faster

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A dip increases the speed (decreasing travel time), but also the distance to travel (increasing travel time). Which of those effects dominates depends on the shape of the dip.

The hill decreases speed and increases distance, so it's always slower than the straight line.

Most things that can fairly be described as a "small dip" should decrease travel time. When I was presented with the problem it came with illustrations to clarify. Surprisingly hard to make it watertight with text alone.

First one depends on the bowling ball. Most alleys have balls ranging from 7lb to 16lb, all the same volume, and the crossover point where they’d sink is 11.6lb.

If it was a floating bowling ball, the lake water level would stay the same when you toss it from a boat. If it were a sinking one, it would decrease.

I think you're counting the overall sphere as the volume, but water would leak in through the finger holes so only their actual material counts. I suspect different weight bowling balls generally have different volumes.

Also if the lake is a mile deep it would pressure the ball more than the air do.

Bowling balls aren't hollow, they're solid spheres with finger holes drilled in. The varying weights comes from having weighted cores inside.

Oh OK thanks, I didn't realise. I just had some fun looking at bowling ball cross sections.

That's why the problem statement specifies that the bowling ball sinks.

Good point! I skimmed over that part, you’re right.

Next bail 10 litres of water from the lake into the open-topped boat.

What are the effects of the 10 litres of air displaced from within the boat?

Lake level stays the same.

Unless there was a butterfly in that part of the air .. not much.

But won't your boat displace more water by lowering a bit if you've got additional mass on board?

That's what they meant by "in boat displaces its weight in water". While it's in the boat, the amount of water it displaces weighs as much as the bowling ball. While it's in the water, it displaces the volume of the bowling ball, and its weight doesn't matter. The ball is denser than water (since it sinks), so the amount of water it displaces based on its weight is bigger than the amount of water it based on its volume.

Ah, that makes sense, thanks.

> Ball is more dense than water

Wouldn't that mean the water level will raise a bit because: displaced weight > displaced volume?

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