The light beacon of a lighthouse is situated a distance 2.00 km from a long, straight shoreline (shortest distance to the shoreline). the light rotates at a rate of 3.00 rev/minute. at a certain time, the illuminated spot on the shoreline is 4.00 km from the lighthouse. how fast is the illuminated spot moving at that point?

In triangle ABC

tanθ = BC/AB

tanθ = x/2

taking derivative both side relative to "t"

sec²θ (dθ/dt) = (0.5) (dx/dt)

sec²θ w = (0.5) v                                eq-1

when x = 4 ,

tanθ = 4/2

θ = tan⁻¹ (2) = 63.4 deg

using eq-1

sec²θ w = (0.5) v  

sec²63.4 (3) (2pi/60) = (0.5) v  

v = 3.13 m/s

the higher the current the higher the mag field around it the higher the influence on the compass

the following is queen elizabeth’s purposes:

- to encourage the parliament that the technique of picking successors to the seat based merely on birthright needs to be reviewed.

- (not) to convince the parliament that her kid should not be measured as a likely choice for heir to the english power.

- to persuade the parliament that merely since she has a child does not assure that the kid will be a capable leader.

- to sway the parliament how shattering it could be if they proceeded discourteously concerning her or her child.