- 14

- 0

hi.

can anyone push me in the right direction with the followin problem, please?

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.

[tex]F = {{dp} \over {dt}}[/tex]

[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??**

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: