Fun math problem!!

This looks like a tricky problem at first, but if you look at it for a min, then you can get it.

A cop car is 60m in front of the wall.  If the siren light is spinning at 20 revolutions per min, and a light beam from the siren light hits the wall at a 60deg angle (meaning the angle between the wall and the light beam is 60deg), find the speed the light beam is moving along the wall at that inst moment.

SHOW ALL WORK!!!

It CAN be done with the information provided, so don't complain.

pi*160/3 m/s

Not showing the work because I'm probably wrong and DO YOUR OWN HOMEWORK.

That's right.  And this was not my hw, it was a problem on a test.

I got v = pi 80/sqrt(3) m/s. I'll just explain how I got it even if I am wrong.

frequency of light = f = 20/ rev/min = 20/60 rev/sec
angular frequency = w = 2 pi f

distance from siren to wall = r = 60/sin(pi/3) = 60/[sqrt(3)/2]

light's velocity on wall = v = w r = [2 pi (20/60)] [60*2/sqrt(3)] = pi 80/sqrt(3)

sort of model for >>4

|
|
|\
| \
|60\ r
|   \
|    \
|     \____
| 60m |car |

Speed of light.

___x___
\pi/3 |
 \    |
  \   |l=60m
   \  |
    \ |
     \|<--a=pi/6
     car
da/dt=2*pi/3s^-1

x=tan(a)*l
dx/dt=l*sec(a)^2*da/dt
dx/dt=(60m)*sec(pi/6)^2*(2*pi/3s^-1)
dx/dt=(pi*40m/s)*(sqrt(3)/2)^2
dx/dt=(pi*40m/s)*3/4
dx/dt=pi*30m/s

>>7
But the light is not going up and down. It is going sideways. So 'a' and 'x' would not change at all.

The speed of light is constant because we cannot divide by zero.

I just had that problem on a test last week.  Except it was the cop car parked 50 feet from the wall and it was making an angle of 30 degrees.  Also, it was .5 revs per seconds.

www.hyperreals.com

Someone confirm >>4,5 will you. >>7 is obviously wrong btw.