OpenStudy (anonymous):

a ball with mass m/2 filled with gas of mass m/2 is kept on a frictionless table . a bullet of mass m/4 and velocity v penetrates the ball and rests at t=0 . the compressed gas is emitted at a const velocity v/2 relative to the ball and at even rate dm/dt=k find the vel of ball as a function of time .

OpenStudy (anonymous):

hi shanur this problem involves conservating linear momentum, so in the first instant the bullet is carrying L.M and shares it with the filled ball , but the ball has been perforated... so the ball ejects mass with velocity v/2 relative to the ball, using a galilean tranform we determine the velocity from an fixed reference frame which is instantaneously Vb-V/2 (Vb = velocity of the ball) since the system ejects mass with constant rate, the mass ejected at time t is simply k*t all this gives: \[L.M_{}=\\ \frac{ m }{ 4 }*V=kt(Vb-V/2)+(2*\frac{ m }{2 } +\frac{ m }{ 4 } - kt)Vb \] some more algebra and we can find Vb (ball velocity) \[Vb=\frac{\left( 2\,k\,t+m\right) \,V}{5\,m}\] this equation works fine if time t is below the value m/(2*k), after that time, the ball is no longer expelling mass the all velocities remain constant. hope all this helps, i'm not sure if my solution is correct this is the first time i deal with a problem like this...

OpenStudy (anonymous):

hmm just now i realize that the solution i gave is wrong! because Vb varies with time, so i was supposed to obtain a diff. equation but i still haven't studied those...

OpenStudy (anonymous):

thanks for your help im trying to understand that even though its not correct