Posted by **Anonymous** on Wednesday, October 19, 2011 at 1:22am.

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 -
**Steve**, Wednesday, October 19, 2011 at 11:49am
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

## Answer This Question

## Related Questions

- Calculus - A lighthouse is located on a small island 3 km away from the nearest ...
- Calculus 1 - A lighthouse is located on a small island 4 km away from the ...
- Calculus - A lighthouse is located on a small island 4 km away from the nearest ...
- Calculus 1 - Related Rates: A lighthouse is located on a small island 4 km away ...
- calculus - a revolving light is located at 5 km from a straight shoreline with a...
- Calc - A lighthouse is fixed 130 feet from a straight shoreline. A spotlight ...
- Calculus - A rotating beacon is located 1 kilometer off a straight shoreline. If...
- Calc - A rotating beacon is located 1 kilometer off a straight shoreline. If the...
- Calculus - Consider the illustration, which shows a rotating beam of light ...
- calculus - Consider the illustration, which shows a rotating beam of light ...

More Related Questions