Calculus

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! :) :)

  • Calculus -

    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?

  • Calculus -

    Sorry, I mean to make a new question, disregard above 'answer'.

  • Calculus -

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

  • Calculus -

    You're a jerk.

  • Calculus -

    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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  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‚Äč lighthouse?

More Similar Questions