Calc

posted by .

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 down the shoreline.

I need to show work, so formatting answers in this manner would be most appreciated. Thanks in advance! :) :)

  • Calc -

    3 rev/min = 6 pi radians/min
    Multiply that by the 1 km radial distance to get the speed the beam apparears to move at that distance:
    6 pi x 1 = 18.85 km/min
    Multiply that by 60 min/hr to get the spped in km per hour

  • Calc -

    I beg to differ with the usually correct drwls.
    This is a related rate problem dealing with angular velocity, so trig will be needed.

    Let the point on the shore be x km down the shoreline.
    so we have a right angled triangle, let the angle at the lighthouse be ß
    we are given dß/dt = 6pi/min

    The tanß = x/1
    and sec^2 ß(dß/dt) = dx/dt

    when x = 1/2 and using Pythagoras I found sec^2 ß = 1.25

    so 1.25(6pi) = dx/dt

    so dx/dt = 23.5629 km/min
    = 1413.72 km/h

  • Calc -

    Reiny is correct; I did not fully read the problem and assumed the shore was perpendicular to the beam

Respond to this Question

First Name
School Subject
Your Answer

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. 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 …
  3. 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 …
  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 searchlight rotates at a rate of 4 revolutions per minute. The beam hits a wall located 9 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per hour) is this dot moving when the angle …
  6. 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?
  7. 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?
  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