Determine the value k0 needed

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Reference no: EM13191822

We need to design a ballistics chamber to decelerate test projectiles fired into it. Assume the resistive force encountered by the projectile is proportional to the square of its velocity and neglect gravity. As the figure indicates, the chamber is to be constructed so that the coefficient k associated with this resistive force is not constant but is, in fact, a linearly increasing function of distance into the chamber. Let k (x) = k0x, where k0 is a constant; the resistive force then has the form k (x)v2 = k0xv2 . If we use time t as the independent variable, Newton's law of motion leads us to the differential equation
m dv/dt + k0xv2 = 0 with v= dx/dt

(a) Adopt distance x into the chamber as the new independent variable and rewrite differential equation (14) as a first order equation in terms of the new independent variable.

(b) Determine the value k0 needed if the chamber is to reduce projectile velocity to 1% of its incoming value within d units of distance.

Reference no: EM13191822

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