Estimate the stopping distance

Reference no: EM13181856

A very small spherical particle (on the order of 5 microns in diameter) is projected into still air with an initial velocity of ν0 m/sec, but its velocity decreases because of drag forces. Its velocity t seconds later is given by ν(t) = ν0e-at for some a > 0, and the distance s(t) the particle travels is given by
s(t) = v0/a(1-e^-at)

The stopping distance is the total distance traveled by the particle.
(a) Find a formula that approximates the stopping distance in terms of ν0 and a.
(b) Use the formula in part (a) to estimate the stopping distance if ν0 = 12 m/sec and a = 1 × 10^5.

Reference no: EM13181856

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