The Rolling Disk
A
diameter disk is moving toward three nails with lengths are
respectively and the distance between first and second nail is
and between the second and third is
.
which nail will be hit first by the disk?
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1 solution
To solve this problem lets calculate D' which is the distance from the nail to the disk-floor contact point for each nail when it is hit by the disk.
Then we calculate D which is the distance from disk-floor contact point to first nail (so we use first nail as a reference).
D 1 = D ′ 1 = 1 2 . 5 2 − ( 1 2 . 5 − 2 ) 2 ≈ 6 . 7 8
D 2 = D ′ 2 − 1 = 1 2 . 5 2 − ( 1 2 . 5 − 4 . 5 ) 2 − 1 ≈ 8 . 6
D 3 = D ′ 3 − 2 . 5 = 1 2 . 5 2 − ( 1 2 . 5 − 6 ) 2 − 2 . 5 ≈ 8 . 1 8
that's mean nail 2 will be hit when the disk is 8.6 cm away from the nail number 1.
So the answer is N a i l . N u m b e r . 2