Solving Velocity of Trolley After Loss of Grains

[The legend]

Homework Statement

A trolley of mass 10 kg has heap of grains of mass 5 kg in it and it is moving with a velocity of 20m/s. There is a hole made then, so that the grains come out at the rate of 0.2m/s. When all the grains fall out, what is the velocity of the trolley?
(Surface is frictionless, and no grains obstructs motion of trolley as they fall down)

Homework Equations

Equations of motion.

The Attempt at a Solution

So the time I got was
5/0.2 = 25 seconds

then i tried to apply conservation of momentum, but that didnt work.
So I used the equation
v=u+at
v=20+a*25

but since this has 2 unknows, i am not understanding how to solve it.
Any help, appreciated!

 

[p21bass]

The question, as stated, doesn't make sense. Is it really 0.2m/s? Or is it 0.2kg/s? If it's the former, you need either the mass of each grain, or total number of grains (so that you can determine mass of one grain).

Do you know (if this is in your textbook) what the answer is supposed to be?

 

[The legend]

oh sorry, it is 0.2 kg/s
the answer is 10m/s

 

[The legend]

though i never understood how the velocity decreased, i thought it would increase actually.
Any help appreciated!

 

[p21bass]

I think your answer book is incorrect. If the grains are falling down (y-direction), and the trolley (with grains) is moving at a constant velocity on a frictionless surface in the x-direction - then there is no force acting in the x-direction to impede/alter the velocity of the trolley.

 

[The legend]

i don't know whether it is right or wrong(the answer). This sum was given to me by a friend and he told me the answer. So are you sure about that, the velocity doesn't change?

 

[The legend]

umm...is the answer really wrong?

 

[rl.bhat]

umm...is the answer really wrong?

I think so.
No external force is acting on the system. So dp/dt = 0.

p = mv

dp/dt = m*dv/dt + v*dm/dt = 0.

dm/dt is constant. Let it be μ.

m*dv/dt = -μ*v.

At any instant m = mo - μ*t.

dv/v = -μ*dt/(mo-μt)

\int_{v_o}^v{\frac{dv}{v}} = \int_0^{25}{\frac{-\mu*dt}{(m_o -\mu*t)}

Solve the integration and find v.

 

[The legend]

Ok, thanks a lot, sir!

 

[Rayquesto]

i thought about using momentum properties to solve this, since the variables involve mass and velocity, but idk. maybe the gravitational force times the amount of time it takes for the grain to fall out can equal the final velocity times mass minus the initial velocity times the mass.