# Calculus

posted by .

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
P

?

• Calculus -

Draw a diagram. If x is the distance from P, and θ is the angle swept out by the beam, measured from the line joining the lighthouse and P,

x/4 = tan θ

dx/4 = sec^2 θ dθ

dx = 4 sec^2 θ * 3 * 2π

So, what is sec θ? tan θ = 1.7/4 = 0.425
sec^2θ = 1+tan^2θ = 1.18

dx = 4*1.18*3*2π = 88.97 mi/min

## 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

Consider the illustration, which shows a rotating beam of light located 0.5 mile from a shoreline. The beam rotates at a rate of 4 revolutions per minute. How fast (in miles per minute) is the distance between the beam and the point …
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

A light in a lighthouse 5 kilometers offshore from a straight shoreline is rotating at 4 revolutions per minute. How fast is the beam moving along the shoreline when it passes the point 5 kilometers from the point opposite the​ lighthouse?

More Similar Questions