Newton second law involving a gallon of water

Only when the mass remains constant does Newton's Second Law of motion reduce to
[tex]\vec{F}=m\vec{a}[/tex]
When dealing with variable mass, use
[tex]\vec{F}=\frac{d}{dt}(m\vec{v})[/tex]

 

No, the mass is not constant. It is changing with time. Also, did you copy the question down fully, and properly?

 

This equation is known to be incorrect in general, although it is true in some cases. Correct classical variable-mass equations of motion were finally well established in the 1990s! Before that, many incorrect results appeared in the published literature. Google 'variable-mass dynamics' for relevant papers.

RGV

 

A couple of questions:

Is this a gallon of water or a kilgram of water? A litre of water has a mass of 1 kg.
If this is a gallon, is this a US gallon [8 lb] or an imperial gallon [10 lb],

EDIT: I ask about which gallon as I don't know where you are posting from.

 

Interesting to know.. Especially considering this was in my Calculus textbook from January 2009.

 

i'm pretty sure that the volume isn't important just the change in mass

 

If the box was not leaking, it would take only about 2 seconds to reach the top, arriving with a velocity of about 10 m/s.

In two seconds, the mass will have reduced from 1.00 kg to 0.98 kg - a very small change, so the final velocity won't be much bigger.
Since data was given to one specific figure only, the answer should be 1 x 10¹ regardless.