- #1

bbal

- 5

- 0

- Homework Statement:
- We have slope, over which there's a point (P). The point is connected to the slope with a straight line. Find the line, a small ball would travel along the fastest.

- Relevant Equations:
- S=(at^2)/2

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- Thread starter bbal
- Start date

- #1

bbal

- 5

- 0

- Homework Statement:
- We have slope, over which there's a point (P). The point is connected to the slope with a straight line. Find the line, a small ball would travel along the fastest.

- Relevant Equations:
- S=(at^2)/2

- #2

DaveC426913

Gold Member

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- 4,951

Show your work so far.

- #3

bbal

- 5

- 0

It's basically all you can see on the picture. I took it as a starting, that if we connect the "top" of a circle to any other point of the circle with a straight line, the time to travel along each would be the same. Then I tried to sketch a circle, such that, point P is on "top" of it and the slope is tangent to it.Show your work so far.

- #4

The obvious, but not particularly elegant, approach, is to consider an arbitrary trajectory at some angle ##\alpha## to the downward vertical through the point P, find the component of gravitational acceleration parallel to the rail, find the length of this rail, and vary ##\alpha## in such a way to minimise the time.

The answer might suggest a simpler line of reasoning! If you remember your circle theorems...

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