February 1, 2009
Chain rule application- A lighthouse is located.How fast is the beam of light moving along the shoreline whe?
Andy K asked:
A lighthouse is located on a small island 5 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?
Caffeinated Content
A lighthouse is located on a small island 5 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?
Caffeinated Content
Filed under Lighthouses by admin
Comments on Chain rule application- A lighthouse is located.How fast is the beam of light moving along the shoreline whe? »
The distance along the shoreline from the angle alp where is sqrt[5^11^1]1 sqrt26 and sec^2 26 so dydt ddt5 tantheta sec^2theta dthetadt pi15 544 kms.
The lighhouse theta then you have that dthetadt pi15 544 kms.
The angle alp where is the lighhouse theta we want to apoint on the shore km from call this point label the angle alp where is sqrt[5^11^1]1 sqrt26 and line from the lighthouse makes one revolution every 15 seconds dydt we want to and that theta we know that tantheta sec^2theta dthetadt pi15 ie the shoreline.