# calculus

posted by .

The beacon on a lighthouse makes one revolution every 20 seconds. The beacon is 300 feet from
the nearest point, P, on a straight shoreline. Find the rate at which the ray of light moves along
the shore at a point 200 feet from P.

• calculus -

Make a sketch, let the distance between the end of the ray of light and point P be x ft
let the angle formed at that moment be Ø
then,
tanØ = x/300
x = 300tanØ
dx/dt =300sec^2 Ø dØ/dt

let the hypotenuse be h
when x=200
h^2 = 200^2+300^2
h = 100√13
secØ = 100√13/300 = √13/3
sec^2 Ø = 13/9
and we are told dØ/dt = 2π/20 rad/sec

dx/dt = 300(13/9)(π/10) = 130π/3 ft/sec

## Similar Questions

1. ### Calculus

A rotating beacon is located 1 kilometer off a straight shoreline. If the beacon rotates at a rate of 3 revolutions per minute, how fast (in kilometers per hour) does the beam of light appear to be moving to a viewer who is 1/2 kilometer …
2. ### Calc

A rotating beacon is located 1 kilometer off a straight shoreline. If the beacon rotates at a rate of 3 revolutions per minute, how fast (in kilometers per hour) does the beam of light appear to be moving to a viewer who is 1/2 kilometer …
3. ### Calc

A lighthouse is fixed 130 feet from a straight shoreline. A spotlight revolves at a rate of 11 revolutions per minute, (22 rad/min ), shining a spot along the shoreline as it spins. At what rate is the spot moving when it is along …
4. ### Calculus

A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline. Its light makes 3 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1.7 kilometers from …
5. ### Calculus

A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
6. ### Calculus

A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes three revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
7. ### calculus

a revolving light is located at 5 km from a straight shoreline with a constant angular velocity. what velocity does the light revolve if the light moves along the shoreline at the rate of 15km/min when the beam of light makes a angle …
8. ### Calculus 1

Related Rates: A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is …
9. ### Calculus 1

A lighthouse is located on a small island 4 km away from the nearest point P on a straight shoreline and its light makes two revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
10. ### Calculus (trig derivatives)

A lighthouse 2 miles offshore has a light that rotates once every 20 seconds. At what rate is the light traveling along the shore if it is shining on a point 4 miles along the shore from the point nearest the lighthouse?

More Similar Questions