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Other math problem
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Posted on: Thu May 04, 2023 3:41 pm

Posts: 20
Joined: Wed Jan 05, 2022 8:59 pm
Other math problem
A prey animal is in the middle of a circular pond. Outside the pond is a predator. The predator can not swim.

The movement speed of the predator is 4 times faster on land then the movement speel of the prey animal in the water.
The pray animal is faster on land.

Can the pray animal escape the predator?

Posted on: Thu May 04, 2023 5:06 pm

Posts: 955
Location: Ukraine
Joined: Tue Mar 01, 2016 10:03 pm
Re: Other math problem
guidocram wrote:
A prey animal is in the middle of a circular pond. Outside the pond is a predator. The predator can not swim.

The movement speed of the predator is 4 times faster on land then the movement speel of the prey animal in the water.
The pray animal is faster on land.

Can the pray animal escape the predator?

On a simplistic level, if the prey animal keeps swimming in a straight line away from the predator’s starting position, it won’t reach the shore in time because the predator will have run pi times r, and pi = 3.14159…

But if the prey animal continuously changes course to swim in the opposite direction to the predator’s new position, then it may be possible for it to escape. But it’s a long time since I did maths in school and I’ve no idea what the formula would be for the distance travelled by both prey and predator in that scenario. It’s probably a calculus problem, but then again, I could be totally wrong.

Posted on: Sat Dec 16, 2023 6:58 am

Posts: 7
Joined: Sun May 01, 2022 9:43 pm
Re: Other math problem
Assuming the pond has radius 1, the prey animal can move to the circle of radius 1/4 and maintain a position opposite the predator.
This is possible because the prey only has 1/4 the distance to travel.
When the prey then makes a mad dash to the edge of the pond farthest from the predator, the prey has to travel a distance of 3/4.
The time for the prey is 3/4 and for the predator is pi/4. Since pi/4 is greater than 3/4, the predator escapes.

If the prey were stupid and ran in a straight line from the centre of the pond, he would get caught.

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