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(1) From assumption (b), show that the radius of the water droplet at time t is r(t) = ()t+ro. %3D (Hint: m = pV,V =tr³, S = 4r²). (2) From assumption (c), the velocity (v) at time (t) of the water droplet is v' + v%3 g. t+To If the water drops from stationary, solve for v(t). (3) Determine the time when the water droplet has evaporated entirely, given that ro 3mm. Then, 10 seconds after the water drops, the radius r = 2mm.

(1) From assumption (b), show that the radius of the water droplet at time t is r(t) = ()t+ro. %3D (Hint: m = pV,V =tr³, S = 4r²). (2) From assumption (c), the velocity (v) at time (t) of the water droplet is v' + v%3 g. t+To If the water drops from stationary, solve for v(t). (3) Determine the time when the water droplet has evaporated entirely, given that ro 3mm. Then, 10 seconds after the water drops, the radius r = 2mm.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.1: Prisms, Area And Volume
Problem 30E: A storage shed is in the shape of a trapezoidal prism. Each trapezoid represents one of its bases....
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A water droplet evaporates before they reach the ground. ond orde E Figure 1: Water droplets [source] In this situation, a few assumptions are made: a) At initial point, a typical water droplet is in sphere shape with radius r and remain spherical while evaporating. b) The rate of evaporation (when it loses mass (m)) is proportional to the surface area, S. c) There is no air-resistance and downward direction is the positive direction. quati To describe this problem, given that p is the mass density of water, rois the radius of water before it drops, m is the water mass, V is the water volume and k is the constant of proportionality. QUESTION: (1) From assumption (b), show that the radius of the water droplet at time t is on er r(t) = () t + ro- %3D (or (Hint: m = pV,V =nr³, S = 4r2). 4 %3D 3 %3D (2) From assumption (c), the velocity (v) at time (t) of the water droplet is ou 3 v' + t+ro If the water drops from stationary, solve for v(t). (3) Determine the time when the water droplet has evaporated entirely, given that ro = 3mm. Then, 10 seconds after the water drops, the radius r = 2mm.
Transcribed Image Text:A water droplet evaporates before they reach the ground. ond orde E Figure 1: Water droplets [source] In this situation, a few assumptions are made: a) At initial point, a typical water droplet is in sphere shape with radius r and remain spherical while evaporating. b) The rate of evaporation (when it loses mass (m)) is proportional to the surface area, S. c) There is no air-resistance and downward direction is the positive direction. quati To describe this problem, given that p is the mass density of water, rois the radius of water before it drops, m is the water mass, V is the water volume and k is the constant of proportionality. QUESTION: (1) From assumption (b), show that the radius of the water droplet at time t is on er r(t) = () t + ro- %3D (or (Hint: m = pV,V =nr³, S = 4r2). 4 %3D 3 %3D (2) From assumption (c), the velocity (v) at time (t) of the water droplet is ou 3 v' + t+ro If the water drops from stationary, solve for v(t). (3) Determine the time when the water droplet has evaporated entirely, given that ro = 3mm. Then, 10 seconds after the water drops, the radius r = 2mm.
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