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vladimir69
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Homework Statement
A fire department's tanker truck has a total mass of 21000kg, including 15000kg of water. Its brakes fail at the top of a long 3 degree slope and it begins to roll downward, starting from rest. In an attempt to stop the truck, firefighters direct a stream of water parallel to the slope beginning as soon as the truck starts to roll. The water leaves the 6cm diameter hose nozzle at 50m/s. Will the truck stop before it runs out of water? If so, when? If not, what is the minimum speed reached?
Homework Equations
[tex]F=ma[/tex]
[tex]F_{net}=\frac{dp}{dt}[/tex]
[tex]\theta=3[/tex]
The Attempt at a Solution
The rate of loss of mass per second is
[tex]\frac{dm}{dt}=50\pi r^2 m^3/s[/tex]
[tex]\frac{dm}{dt}=141 kg/s[/tex]
So after 15000/141=106 seconds the fire truck will have run out of water.
The only other force acting is gravity. (not sure why friction isn't included)
so
[tex]F_{net}=m(t)g\sin\theta-141 \times 50=(21000-141t)g\sin\theta-7050[/tex]
for [tex]0\leq t\leq 106[/tex]
Fire truck will stop next when a=0 which occurs at
[tex]0=(21000-141t)g\sin\theta-7050[/tex]
[tex]141t=7257[/tex]
[tex]t=51.5s[/tex]
51.5 < 106
So i say yes the fire truck will stop before it runs out of water
Does my argument sound ok ?