Lighthouses Round Island
Wednesday, July 6th, 2011lighthouses round island
 |
No items matching your keywords were found.
Related Rates! Lighthouse question...?
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? (Round your answer to one decimal place.)
___?___km/min
Take the line through the lighthouse and P as the starting axis.
Then if the beam of light makes an angle θ radians with the axis,
the angle is changing at the rate of 4*2π/60 radian per second.
(or 8π radian/minute)
i.e. dθ/dt = 2π/15 [or 8π if using minute]
Now when the beam of light strikes a point x km from P,
tan θ = x/3
Therefore
sec²θ dθ/dt = (1/3)dx/dt
hence
dx/dt = 3*(1 + x²/9)*dθ/dt
When x = 1 this has the value
dx/dt = 3(1 + 1/9)*2π/15 or, if using minute as the time unit, 3*(10/9)*8π
........ = 4π/9, or, if using minute as the time unit, 80π/3
This represents a speed of
1.396 km/s, which is
83.8 km/minute correct to 1 decimal place.
 |
Mystery at Round Island Light (Mackinac Passage (Unnumbered)) List Price: $10.00 Sale Price: $5.63  |
|
Fifteen-year-old Pete Jenkins and his three summer friends visit the nearby Round Island Lighthouse after crossing the turbulent water of Lake Huron in their tiny dingy. After exploring the island they return to find their picnic basket turned upside down and a warning message in their boat... |
 |
Spoontiques Lighthouse - Round Island Light, MI Sale Price: $18.99 |
 |
Round Island Lighthouse Michi American flag White T-Shirt by CafePress List Price: $29.50 Sale Price: $20.00 |
|
You wouldn't judge a book by its cover, just as you wouldn't judge a person by their shirt. No wait, yes you would. This is anything but a plain white-t. Be comfortable in this cotton shirt, and show off your style and personality in the process... |
 |
ROUND ISLAND MI LIGHTHOUSE TAPESTRY THROW 50" x 60" Sale Price: $37.49 |
 |
Spoontiques Lighthouse - Round Island, MS Sale Price: $14.99 |
 |
Round Island Lighthouse Michi American flag Dark T-Shirt by CafePress List Price: $29.50 Sale Price: $22.50 |
|
Look cool without breaking the bank. Our durable, high-quality, pre-shrunk 100% cotton t-shirt is what to wear when you want to go comfortably casual. Preshrunk, durable and guaranteed.5.6 oz. 100% cottonStandard fit American flag Tee, TShirt, Shirt... |
 |
Round Island, Michigan LIGHTHOUSE Suncatcher Window 11x22 Glass Panel Framed Sale Price: $69.95 |
|
** PURCHASE by 12/15 for CHRISTMAS DELIVERY! ** Wood-framed in high-quality Wisconsin hardwood, this panel of art glass measures 11.5" wide x 22.5" high, and comes with frame-top hooks & chain for hanging... |
 |
Round Island Lighthouse Michi American flag Light T-Shirt by CafePress List Price: $29.50 Sale Price: $20.00 |
|
Look cool without breaking the bank. Our durable, high-quality, pre-shrunk 100% cotton t-shirt is what to wear when you want to go comfortably casual. Preshrunk, durable and guaranteed.5.6 oz. 100% cotton Standard fit American flag Tee, TShirt, Shirt... |
 |
Harbour Lights "Round Island, MI" HL153 Lighthouse Sale Price: $52.32 |
|
This lighthouse was a 1995 Limited Edition of 7,948. |
 |
Photographic Prints of Round Island with lighthouse, Isles of Scilly, Cornwall, United Kingdom, Europe from Robert Harding Sale Price: $15.99 |
|
10x8 Print, Round Island with lighthouse, Isles of Scilly, Cornwall, United Kingdom, Europe. Round Island with lighthouse, Isles of Scilly, Cornwall, United Kingdom, Europe. Chosen by Robert Harding. High quality RA4 prints... |