Angular Speed

Hi everyone... new to the forum but I've read posts before that have helped me out a lot.

A patrol car is parked 50' from a long warehouse. The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write theta as a function of x. How fast is the light beam moving along the wall when the beam makes an angle of theta = 45 degrees with the line perpendicular from the light to the wall.

I'm kind of lost as to where to even start here. I know I'm looking for dx/dt.

do I start by saying tan(theta) = x/50
theta = [arctan](x/50)

then differentiate that dtheta/dt (which is 30) = d/dx [arctan](x/50)

u = (x/50) so u' = 1/50

30 = (1/50)/[1+(x/50)^2]

Trying to see if I'm on the right path here, and if so, what is the next step. Any help would be greatly appreciated.

Thanks,
MJ

Quote:

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Originally Posted by MJ320

Hi everyone... new to the forum but I've read posts before that have helped me out a lot.

A patrol car is parked 50' from a long warehouse. The revolving light on top of the car turns at a rate of 30 revolutions per minute. Write theta as a function of x. How fast is the light beam moving along the wall when the beam makes an angle of theta = 45 degrees with the line perpendicular from the light to the wall.

I'm kind of lost as to where to even start here. I know I'm looking for dx/dt.

do I start by saying tan(theta) = x/50
theta = [arctan](x/50)

then differentiate that dtheta/dt (which is 30) = d/dx [arctan](x/50)

u = (x/50) so u' = 1/50

30 = (1/50)/[1+(x/50)^2]

Trying to see if I'm on the right path here, and if so, what is the next step. Any help would be greatly appreciated.

Thanks,
MJ

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everything is ok except for ... you have to convert 30 rpm to units of rad/min.

will be in ft/min

Awesome. I had actually thought about that too, but wanted to at least make sure I was on the right path. Thanks.