An object of mass m is released from rest in a medium in which the frictional forces are
Chapter 1, Problem 15(choose chapter or problem)
An object of mass m is released from rest in a medium in which the frictional forces are proportional to the square of the velocity. The initial-value problem that governs the subsequent motion is mv dv dy = mg kv2, v(0) = 0, (1.12.6) where v(t) denotes the velocity of the object at time t, y(t) denotes the distance travelled by the object at time t as measured from the point at which the object was released, and k is a positive constant. (a) Solve (1.12.6) and show that v2 = mg k (1 e2ky/m). (b) Make a sketch of v2 as a function of y.
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