Find velocity of boat as function of the time

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Homework Help Overview

The problem involves a motorboat moving on a lake with an initial velocity and experiencing resistance proportional to its velocity after the engine is shut down. The subject area pertains to dynamics and forces acting on moving objects.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the forces acting on the boat, questioning the inclusion of gravitational force in the analysis and its relationship to the resistance force. There is uncertainty about the correct application of vector components in the context of the problem.

Discussion Status

The discussion is exploring different interpretations of the forces involved, particularly regarding the relevance of gravitational force and its direction relative to the resistance force. Some participants are providing guidance on considering vector components.

Contextual Notes

There is a mention of equilibrium with buoyancy, indicating that certain forces may be balanced, which could affect the analysis of the problem. The original poster expresses uncertainty about their approach.

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Homework Statement


a motorboat of mass m moves along a lake with velocity Vi. at the moment t=0 the engine of the boat is shut down, assuming the resistance of water to be proportional to the velocity of the boat f= -rv , find the velocity of the boat as a function of time

Homework Equations


ƩF = ma
a = dv/dt

The Attempt at a Solution


ƩF = ma
- mg - rv = ma
dv/dt = (-mg - rv)/m
am not sure if i am going the right way or not
 
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Hello.

Force and acceleration are vector quantities. You should work with components:

ΣFx = max

ΣFy = may
 
I think that you should not consider mg as it is in 90° angle with rv
 
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Niladri Dan said:
I think that you should not consider mg as it is in 90° angle with rv
And it is in equilibrium with buoyancy.
 
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