Help with Maths Question (1 Viewer)

[lilainjel]

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.

Thanks.

 

[lolokay]

distance, D, from P to a certain point = 180tan[x], where x is the angle between the ray of light and the line drawn from L to P
The light has a period of 10 seconds (goes 2pi in 10s)
so dx/dt = pi/5
dt/dx = 5/pi
D=180tan[x]
x = arctan[D/180]
dx/dD = 1/(180 + D²/180)
dD/dt = (180 + D²/180)pi/5
when D = 300,
= 136pi

 

[Aerath]

Heh - thank god this is 3U. I thought it was 2U, and I was like...shiiit, can't do it.