Chapter 6, Problem 43AP

A seaplane of total mass m lands on a lake with initial speed $v_i\hat{i}$. The only horizontal force on it is a resistive force on its pontoons from the water. The resistive force is proportional to the velocity of the seaplane: $\stackrel{\to }{R}=-h\stackrel{\to }{v}$. Newton’s second law applied to the plane is $-bv\hat{i}=m(dv/dt)\hat{i}$. From the fundamental theorem of calculus, this differential equation implies that the speed changes according to

${\displaystyle {\int }_{v_i}^v\frac{dv}{v}=-\frac{b}{m}{\displaystyle {\int }_0^{t}dt}}$

(a) Carry nut the integration to determine the speed of the seaplane as a function of time. (b) Sketch a graph of the speed as a function of time. (c) Does the seaplane come to a complete stop after a finite interval of time? (d) Does the seaplane travel a finite distance in stopping?