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 Bouncy Bouncy revisited (Posted on 2006-03-23)
In Bouncy Bouncy Part 1 you were to find the equation for the path of a laser reflected off of a flat mirror. The slopes of each were specified.

The challenge now is to find a general formula for the new slope of any laser with slope a reflecting off a mirror of slope b.

Use of trigonometry is acceptable, but not required.

 No Solution Yet Submitted by Jer Rating: 1.5000 (2 votes)

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 Solution Comment 1 of 1
` `
`Let a' be the slope of the reflected laser.`
`Clearly, arctan(a) + arctan(a') = 2 arctan(b).`
`Applying the trig. identity for the tangent ofthe sum of two angles to this gives`
`   a + a'        2b  --------- = ---------   1 - aa'     1 - b^2`
`Solving for a' gives`
`        b(ab + 2) - a  a' = ---------------        b(2a - b) + 1`
` `

 Posted by Bractals on 2006-03-23 21:40:57

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