An object moving in a liquid experiences a linear drag force:

= (bv, direction opposite the motion), where b is a constant called the drag coefficient. For a sphere of radius R, the drag constant can be computed as b = 6phR, where h is the viscosity of the liquid.

a. Find an algebraic expression for v_x(t), the x-component of velocity as a function of time, for a spherical particle of radius R and mass m that is shot horizontally with initial speed v₀ through a liquid of viscosity h.

b. Water at 20^o­C has viscosity h = 1.0 = 10^-3 N s/m². Suppose a 4.0-cm-diameter, 33 g ball is shot horizontally into a tank of 20­^oC water. How long will it take for the horizontal speed to decrease to 50% of its initial value?