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Conservation of Momentum

  • Thread starter Gregie666
  • Start date
14
0
hi.
can anyone push me in the right direction with the followin problem, please?

1. Homework Statement
a cart is moving on a frictionless surface at a speed of [tex]V_0 [/tex]
the mass of the cart is M.
it suddenly starts to rain at time t=0. the rain is dropping vertically at a rate of q gk per second.
the cart collects all the rain drops that hit it.
express the speed of the cart as a function of time passed since it started raining.

2. Homework Equations
[tex]F = {{dp} \over {dt}}[/tex]



3. The Attempt at a Solution
[tex]


& F = {{dp} \over {dt}} \Rightarrow \cr
& 0 = {{dm} \over {dt}}v(t) + {{dv} \over {dt}}m(t) \Rightarrow \cr
& 0 = qv(t) + {{dv} \over {dt}}(M + qt) \Rightarrow \cr
& qv = - {{dv} \over {dt}}(M + qt) \Rightarrow \cr
& qvdt = (M + qt)dv


[/tex]

so i get this equation and i dont know how to solve it for v...


**how do i add line breaks to the latex??**
 
Last edited:

Answers and Replies

just like any differential equation, split the variables, put in the initial conditions, and rearrange for the variable you want.

[tex] \int { \frac {q}{M+qt}} dt = \int {\frac {1}{v}}dv [/tex]

Try it that way
 

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