# Toboggan down icy slope

1. Oct 22, 2007

### karnten07

1. The problem statement, all variables and given/known data

a 5.4kg toboggan carrying 35kg of sand slides from rest down an icy 90m slope inclined at 30 degrees below the horizontal. The sand leaks from the back of the toboggan at a rate of 2.3kgsec^-1. How long does it take the toboggan to reach the bottom of the slope?

2. Relevant equations
previous equations involved rockets and the equation:

v(final) = v(initial) + u ln(mi/mf)
where u is the exhaust speed

not sure if this relates to this question though?

3. The attempt at a solution

I drew the situation but cant see how to find the time, any suggestions please?

2. Oct 22, 2007

### learningphysics

Seems like a trick question. Is the sand just leaking out? or is it thrust out with a velocity relative to the toboggan? if it is just leaking then it has exactly the same velocity the moment it is leaked, as when it was still in the tobaggan...

so by conservation of momentum... the toboggan's velocity doesn't change when the sand is released... it is just like if you're travelling in a toboggan horizontally... and you start dropping objects to the ground... you won't speed up...

also although gravity and normal force change because of the decreased mass... the acceleration doesn't...

If it is just leaking out, then it won't affect the speed of the toboggan... it's just a purely kinematics problem... the 2.3kgs^-1 is unnecessary information.

Hope I'm not misunderstanding the question...

3. Oct 22, 2007

### karnten07

I think youre right because the lesson coordinator said something about it not changing, but i wasnt paying full attention. SO if acceleration remains constant could i just use the equation of motion s = 0.5at^2 ?

4. Oct 22, 2007

### learningphysics

yes. be careful about the a... what is the acceleration here?

5. Oct 22, 2007

### karnten07

6. Oct 22, 2007

### learningphysics

7. Oct 22, 2007

### Dick

8. Oct 22, 2007

### learningphysics

9. Oct 22, 2007

### learningphysics

but that's only in the case of friction right? this is frictionless...

10. Oct 23, 2007

### Dick

You are right, of course. That's complete nonsense. How can something accelerate faster than g by passively falling apart? Nothing like one last great good idea before going to bed... Sorry.