Sliding blocks

Classical Mechanics Level 5

On a late rainy night in the 2D Cartesian plane, a carpenter is working on top a slanted roof with two perfectly rectangular cinder blocks. He then places the blocks such that their shorter sides are adjacent to the roof, with the larger block at the top of the roof and the smaller block just below it.

Unfortunately, the larger block begins to slip at a constant rate of 1 inch per second along the roof. The carpenter notices this and quickly and stops the block from sliding any further. To his amazement, when he places a wooden board resting on top the blocks, it's perfectly parallel to the X-axis.

For how long did the block slide from the moment both blocks' centers of mass were co-linear on a vertical line till the moment of stopping?


The blocks magically pass through eachother when the larger block begins sliding, this does not have an effect on either block's momentum.

Answer in seconds and round to be nearest tenths

One cinder block is 1 inch wide and 5 inches tall while the other is 2 inches wide and 10 inches tall.

The roof is defined by the function \(y=-\dfrac{x}{\sqrt3}\)


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