Existence and Uniqueness Theorem. A motorboat of total mass m = 200kg is facing the shoreline and drifting away at 0.5 m/s. In order to return to shore you apply a constant force of 100 Newtons in the direction of the shore. However, the boat is also subject to a drag force of 400v² where v is the velocity in m/s. (a) Find the ODE satisfied by v(t), the velocity in the direction away from the shore, where t is measured in seconds. (b) Find v(t). (c) How many seconds pass before the boat starts heading toward the shore?

Existence and Uniqueness Theorem. A motorboat of total mass m = 200kg is facing the shoreline and drifting away at 0.5 m/s. In order to return to shore you apply a constant force of 100 Newtons in the direction of the shore. However, the boat is also subject to a drag force of 400v² where v is the velocity in m/s. (a) Find the ODE satisfied by v(t), the velocity in the direction away from the shore, where t is measured in seconds. (b) Find v(t). (c) How many seconds pass before the boat starts heading toward the shore?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 42P: A landscape architect is planning an artificial waterfall in a city park. Water flowing at 1.70 m/s...

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