 #1
annamal
 338
 28
 Homework Statement:
 A small diamond of mass 10.0 g drops from a swimmer’s earring and falls through the water, reaching a terminal velocity of 2.0 m/s. a) Assuming the frictional force on the diamond obeys what is b? (b) How far does the diamond fall before it reaches 90 percent of its terminal speed?
 Relevant Equations:

v_t = terminal velocity
a) m*g + b*v = m*a = 0 for terminal velocity
b = m*g/v_t
b) My question is here:
0.9v_t = v0 + a*t = a*t
t = 0.9v_t/a
delta_h = v0*t + 0.5*a*t^2 = 0.5*a*t^2 = 0.5*((0.9*v_t)^2)/a =
where a = (m*g + b*v)/m
delta_h = (0.5*((0.9*v_t)^2)*m)/(m*g + b*v)
plugging in everything delta_h = 1.65 m which is not what the answer is. Please help
b) My question is here!
0.9v_t = v0 + a*t = a*t
t = 0.9v_t/a
delta_h = v0*t + 0.5*a*t^2 = 0.5*a*t^2 = 0.5*((0.9*v_t)^2)/a =
where a = (m*g + b*v)/m
delta_h = (0.5*((0.9*v_t)^2)*m)/(m*g + b*v)
plugging in everything delta_h = 1.65 m which is not what the answer is. Please help
0.9v_t = v0 + a*t = a*t
t = 0.9v_t/a
delta_h = v0*t + 0.5*a*t^2 = 0.5*a*t^2 = 0.5*((0.9*v_t)^2)/a =
where a = (m*g + b*v)/m
delta_h = (0.5*((0.9*v_t)^2)*m)/(m*g + b*v)
plugging in everything delta_h = 1.65 m which is not what the answer is. Please help