What am I doing wrong? "How fast is the light beam moving along the wall when...?"

[Frenchi33]

What am I doing wrong? "How fast is the light beam moving along the wall when...?"

A patrol car is parked 30 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes angles of θ = 45°, θ = 60°, and θ = 80° with the line perpendicular from the light to the wall? (Round your answers to two decimal places.)

(1) I converted from degrees to radians --> "30 rev/min = 60pi rad/min"

(2) I came up with a formula --> "sec^2(theta) * d(theta)/dt = 1/30 * dx/dt"

(3) Then I changed that to "30/cos^2(theta) * d(theta)/dt = dx/dt"

(4) Next, I plug in everything for the first angle of theta, so... "30/cos^2(45) * 60pi = dx/dt"

And I get "dx/dt = 20491.38052", which rounded to two decimal places is "dx/dt = 20491.38", but that's not right on my e-homework submission. This isn't only wrong for when (theta) = 45 degrees. It's wrong for 60 degrees and 80 degrees as well, so I assume I have an error in the formula or something? Please help!!

Thank you.

 

[stapel]

A patrol car is parked 30 feet from a long warehouse (see figure). The revolving light on top of the car turns at a rate of 30 revolutions per minute. How fast is the light beam moving along the wall when the beam makes angles of θ = 45°, θ = 60°, and θ = 80° with the line perpendicular from the light to the wall?

What is shown in the "figure"? Thank you!

 

[Frenchi33]

What is shown in the "figure"? Thank you!

#43 on pg.160, The numbers are different on my e-homework, but it's the same illustration.

https://books.google.com/books?id=d... your answers to two decimal places.)&f=false

Thanks!

 

[stapel]

#43 on pg.160, The numbers are different on my e-homework, but it's the same illustration.

https://books.google.com/books?id=d... your answers to two decimal places.)&f=false

Okay, so you've got the following situation:

diagram:

   light
     *
     |\
   50| \<=beam
     |  \
---------------
  long wall

1. I agree with the conversion to 60pi rads per minute. So they've given us d(theta)/dt = 60pi.

2. How did you obtain this equation? What were your steps?

Thank you!