You and your friend peter are putting new shingles on a roof pitched at 20°. you're sitting on the very top of the roof when peter, who is on the edge of the roof, 5.1 m away, asks you for the box of nails. rather than carry the 2.2 kg box of nails down to peter, you decide to give the box a push and have it slide down to him.
if the coefficient of kinetic friction between the box and the roof is 0.53, with what speed should you push the box to have it gently come to rest right at the edge of the roof?

vi = 3.95 m/s

Explanation:

We can apply the Work-Energy Theorem as follows:

W = ΔE = Ef - Ei

W = - Ff*d

then

Ef - Ei = - Ff*d  

If

Ei = Ki + Ui = 0.5*m*vi² + m*g*hi = 0.5*m*vi² + m*g*hi = m*(0.5*vi² + g*hi)

hi = d*Sin 20º = 5.1 m * Sin 20º = 1.7443 m

Ef = Kf + Uf = 0 + 0 = 0

As we know,   vf = 0  ⇒ Kf = 0

Uf = 0  since hf = 0

we get

W = ΔE = Ef - Ei = 0 - m*(0.5*vi² + g*hi)  ⇒   W = - m*(0.5*vi² + g*hi)   (I)

If

W = - Ff*d = - μ*N*d = - μ*(m*g*Cos 20º)*d = -  μ*m*g*Cos 20º*d    (II)

we can say that

- m*(0.5*vi² + g*hi) = -  μ*m*g*Cos 20º*d  

⇒ vi = √(2*g*(μ*Cos 20º*d - hi))  

⇒ vi = √(2*(9.81 m/s2)*(0.53*Cos 20º*5.1m - 1.7443 m)) = 3.95 m/s

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water