Applications of Trig Question from Cambridge (1 Viewer)

[phoenix159]

A rotating light L is situated at sea 180 metres from the nearest point P on a straight shoreline. The light rotates through one revolution every 10 seconds. Show that the rate at which a ray of light moves along the shore at a point 300 metres from P is (136) pi m/s.

So far I have:

1 revolution / 10 seconds = 2 pi radians / 10 seconds = 0.2 pi rad / second

and a

 

[hayabusaboston]

dx/dt is equal to dx/dtheta times dtheta/dt yes?

tantheta is 300/180, but u want dx/dtheta, so rather than having 300/180 have x/180, as per ur diagram. Differentiate, and rearrange, for 180sec^2(theta)=dx/d(theta)

tan goes to sec^2, and x/180 just becomes 1/180

U found d(theta)/dt to be 0.2 pi, so times together for answer. for theta, u want theta to be as it is at the instant u drew ur diagram, in which tantheta was 300/180, so theta is tan^-1 of that, and sub that theta in to get 136 pi.

Tell me if u dont get anything in there I can reexplain, or someone can use latex lol.

 

[phoenix159]

Thanks!