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$1)$ A $0\mathrm{.}05$ diameter spherical particle with specific gravity $2\mathrm{.}5$ is ejected from an exhaust pipe into standard air at a velocity of $15$ m$/$s$.$

a$)$ Calculate the travel distance before it is stopped by viscous friction? If we ignore the effect of gravity.

b$)$ How long does it take for the particle to come to $5\%$ of its initial velocity?

c$)$ Suppose a large ball $($of diameter $75$ mm and $150$ g$)$ is injected at the same velocity into a tank filled with a viscous fluid, and it stops after $6$ meters, calculate the viscosity of the fluid.