"a spherical water tank, 24 ft in diameter, sits atop a 60 ft tower. the tank is filled by a hose attached to the bottom of the sphere. if a 1.5 horsepower pump is used to deliver water up to the tank", how long will it take to fill the tank?

time taken =10.86 hrs

Explanation:

Since the tank is spherical, we will calculate the volume of a sphere

The radius of the tank, r = Diameter/2

r = 24/2 = 12 ft

Volume , V = 4/3 πr³

V = 4/3 * π * 12³

V = 7238.23 ft³

1 ft = 0.3048 m

V = 7238.23 * (0.3048)³

V = 204.96 m³

Density of water, ρ = 1000 kg/m³

Density = mass/volume

ρ = M/V

Mass, M =  ρ V

Mass = 1000 * 204.96

Mass = 204960 kg

The center of gravity of the tank is at the center of the spherical tank

Height of the center of the tank, h = 12 + 60 = 72 ft

h = 72 * 0.3048

h = 21.75 m

Workdone by the pump,W= mgh

W = 204960 * 9.81 * 21.75

W = 43731802.8 Joules

Power = Work/time

The pump capacity = 1.5 hp

1 hp = 745.7 W

1.5 hp = 1118.55 W

Pt = W

1118.55 * t = 43731802.8

t = 43731802.8/1118.55

t = 39098.62 s

t = 39098.62/3600

t = 10.86 hrs

you'd use the equation that establishes a relationship between  energy  and  wavelength, which looks like this

e=h⋅cλ, where

λ  - the wavelength of the photon; c  - the speed of light, usually given as  3⋅108m/s; h  -  planck's constant, equal to  6.626⋅10−34j s

plug the value you were given for the energy of the photon in the above equation to get the wavelength

e=h⋅cλ⇒λ=h⋅ce

λ=6.626⋅10−34js⋅3⋅108ms−1.257⋅10−24j=1.581⋅10−1m