Calculate the velocity of the boat

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The discussion focuses on calculating the velocity of a boat after a child throws a package from it. Participants confirm that conservation of momentum should be used, considering the combined mass of the child and boat. The initial momentum of the package is calculated as 64 kg·m/s, leading to a derived velocity for the boat of approximately 0.9 m/s. Additionally, there is a brief mention of a second problem regarding the increase in braking distance when a car's speed is increased by 50%, with hints provided on how to relate kinetic energy to braking distance. The conversation highlights the importance of careful calculations and avoiding common errors in physics problems.
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1. A child in a boat throws a 6.40-kg package out horizontally with a speed of 10.0 m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26.0 kg, and that of the boat is 45.0 kg. Ignore water resistance.
Should I use conservation of momentum to solve it? But here the two objects are package and boat? how about the child?
2. If the speed of a car is increased by 50%, by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore the driver's reaction time.
I have no any clue for this one.
Hope you can give me some hint, thanks.
 
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Should I use conservation of momentum to solve it?
Yes.
But here the two objects are package and boat? how about the child?
Here if the child remains at rest while throughing the packet, then you have to consider the combined mass of child and boat.
In problem 2, calculate the increase in the KE when the speed increases by 50% and see how the KE and braking distance are related
 
I have not considered #2 but for #1, is not time information needed (acceleration of the package / time taken for it to reach 10 m/s) in order to answer the question?
 
Please excuse my cerebral lapse. Of course, velocity can be calculated by dividing momentum over mass. So the momentum of the stone, 6.4 kg ms, over the combined mass of the child and boat would give the boat a velocity of 6.4 / 71 = ~0.09 m/s, ignoring resistance.
 
MIA6 said:
1. A child in a boat throws a 6.40-kg package out horizontally with a speed of 10.0 m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. .

I think you have a little math error, you've stated the momentum is 6.4 kg m/s, but you perhaps forgot to multiply the 6.4 kg by 10 m/s?

Or is it me, I'm a little rusty.
 
Yet another failure on my part. I have lost so many marks through silly errors such as this. The answer, unless I am again mistaken is:

V = p/m = (6.4 * 10) / 71 = 64 / 71 = ~0.9 m/s
 
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