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 down the shoreline.

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

  1. 👍 0
  2. 👎 0
  3. 👁 322
  1. Evaluate the limit as h -> 0 of:

    [tan (pi/6 + h) - tan(pi/6)]/h

    I thought the answer was √3/3, or tan(pi/6, but apparently that is wrong, any tips here?

    1. 👍 0
    2. 👎 0
  2. Sorry, I mean to make a new question, disregard above 'answer'.

    1. 👍 0
    2. 👎 0
  3. Gee, now you're going to make people who open this topic think the answer has already been provided. Thanks a ton...

    1. 👍 0
    2. 👎 0
  4. You're a .

    1. 👍 0
    2. 👎 0
  5. tan(θ)=x/1
    cos(θ)=1/sqrt(x^2+1)
    sec^2(θ)=x^2+1

    dθ/dt=3 rev/min=6π rad/min

    x=tan(θ)
    dx/dt=sec^2(θ) dθ/dt

    At x=0.5 km

    dx/dt=(0.5^2+1)*6π=23.6 km/min=1414 kph

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    As seismological station is located at (0,-4) 4 kilometers away from a straight shoreline where the x-axis runs through. The epicenter of the earthquake was determine to be 10 kilometers away from the station. a. Find the equation

  2. 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

  3. Calculus

    A small resort is situated on an island that lies exactly 6 miles from P, the nearest point to the island along a perfectly straight shoreline. 10 miles down the shoreline from P is the closest source of fresh water. If it costs

  4. 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

  1. 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?

  2. 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​

  3. Physics

    A woman runs a kilometer using a force of 210 N and a power output of 500 W. How long in minutes does it take this woman to complete 1 kilometer?

  4. 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

  1. 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?

  2. Pretty pleaaase Help

    As you watch a surfer ride a wave toward the shoreline, what is the shoreline. a. reference point b.distance being travled c.delta d.displacement refrence

  3. Math

    A boat is sailing due east parallel to the shoreline at a speed of 10 miles per hour. At a given time the bearing to the lighthouse is S 70 degrees E, and 15 minutes later the bearing is S 63 degrees E. Find the distance from the

  4. Math

    A lighthouse rotates its light in a circular motion with a constant speed. If the beacon of light completes one rotation every 25 seconds, what is the angular speed of the beacon in radians per minute?

You can view more similar questions or ask a new question.