- #1

JohnLCC517

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**1. In general, dense fluids (such as water) produce a drag force that is directly proportional to the speed of an object moving through them. Suppose a boat is moving through the water and experiencing a fluid drag force of F=-8 v. Suppose the boat has a motor which can output up to 450 Newtons of force. What is the maximum speed of the boat? If the boat starts from rest at t=0, find the speed of the boat as a function of time.**

**2. To get started I am inclined to find velocity, however, I am not aware of any way in which I can find velocity from force (the 450 Newtons of force output by the motor).**

**3. My initial attempt would be to enlist Newton's 3rd law and set up the equation 450 N = 8v (negative sign removed since the velocity will be measured in the positive direction. From there I could find v as follows; (450 N/8) = v which would further suggest that v = 56.25 N. This would create a drag force equal to the force propelling the boat through the water. From here I'm thinking that I should put my findings into a kinematics equation but there appears to not be enough information to do so. Am I missing something crucial?**