Question

A seaplane of total mass $m$ lands on a lake with initial speed $v_{i}$ 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: $\overline{\mathbf{R}}=-b \overrightarrow{\mathbf{v}}$ . Newton's second law applied to the plane is $-b v \hat{\mathbf{i}}=m(d v / d t) \hat{\mathbf{i}}$ . From the fundamental theorem of calculus, this differential equation implies that the speed changes according to $$\int_{v_{i}}^{v} \frac{d v}{v}=-\frac{b}{m} \int_{0}^{t} d t$$ (a) Carry out 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?

          A seaplane of total mass $m$ lands on a lake with initial speed $v_{i}$ 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: $\overline{\mathbf{R}}=-b \overrightarrow{\mathbf{v}}$ . Newton's second law applied to the plane is $-b v \hat{\mathbf{i}}=m(d v / d t) \hat{\mathbf{i}}$ . From the fundamental theorem of calculus, this differential equation implies that the speed changes according to $$\int_{v_{i}}^{v} \frac{d v}{v}=-\frac{b}{m} \int_{0}^{t} d t$$
(a) Carry out 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?

Added by Crystal M.

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