Find velocity of boat as function of the time

In summary, the problem involves a motorboat with mass m moving at velocity Vi on a lake. When the engine is shut down at t=0, the resistance of water is proportional to the boat's velocity, given by f= -rv. Using ΣFx = max and ΣFy = may, the equation for acceleration can be derived as dv/dt = (-mg - rv)/m. However, the force of gravity, mg, may not need to be considered as it is in 90° angle with rv and is in equilibrium with buoyancy.
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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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  • #2
Hello.

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

ΣFx = max

ΣFy = may
 
  • #3
I think that you should not consider mg as it is in 90° angle with rv
 
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  • #4
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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1. What is the formula for finding the velocity of a boat as a function of time?

The formula for finding the velocity of a boat as a function of time is v(t) = d(t)/t, where v(t) is the velocity, d(t) is the distance traveled, and t is the time elapsed.

2. How do you determine the distance traveled by a boat as a function of time?

The distance traveled by a boat can be determined by multiplying the velocity by the time elapsed. Therefore, the formula for distance as a function of time is d(t) = v(t)*t.

3. Can the velocity of a boat change over time?

Yes, the velocity of a boat can change over time due to factors such as wind, currents, and changes in direction. This is why it is important to calculate velocity as a function of time rather than just a single value.

4. How do you plot the velocity of a boat over time?

To plot the velocity of a boat over time, you would first need to collect data on the distance traveled at different time intervals. Then, using the formula v(t) = d(t)/t, you can calculate the velocity for each time interval and plot it on a graph with time on the x-axis and velocity on the y-axis.

5. Can the velocity of a boat be negative?

Yes, the velocity of a boat can be negative if it is moving in the opposite direction of its initial motion. For example, if a boat starts moving east at a velocity of 10 m/s and then changes course to move west at a velocity of 5 m/s, its velocity would be negative (-5 m/s) in relation to its initial motion.

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