6) challenge problem: in searching the bottom of a pool at night, a

watchman shines a narrow beam of light from the flashlight, 1.3 m above the

water level, onto the surface of the water at a point 2.5 m from his foot at the

edge of the pool. where does the spot of light hit the bottom of the pool,

measured from the bottom of the wall beneath his foot, if the pool is 2.1 m deep?

7.08 m

Explanation:

(If we ignore the refraction of light)

There will form two triangles one at the top of pool (torch, edge of pool and point of incidence at top of pool) and one at the bottom of pool (torch, edge of pool and point of incidence at bottom of pool) .

first triangle at the top of pool (torch, edge of pool and point of incidence at top of pool)

First we need to find the angle of incidence:

Height = perpendicular =  1.3 m

Point of incidence = base= 2.5 m

now

tan∅= perpendicular / base

∅= tan⁻¹ (perpendicular / base)

∅=tan⁻¹ (1.3/2.5)

∅= 27.5°

Now 2nd triangle at the bottom of pool (torch, edge of pool and point of incidence at bottom of pool)

Height = perpendicular =  1.3 m + 2.1 m= 3.4 m (torch height + depth of pool)

∅= 27.5°

Spot of light hit bottom of pool= base=?

tan∅ = perpendicular / base

base = perpendicular / tan∅

base = 3.4/tan(27.5°)

base= 7.08 m

Spot of light hit bottom of pool= base= 7.08 m

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this