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Bouncy Bouncy revisited (Posted on 2006-03-23) Difficulty: 3 of 5
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 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 of
the 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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