Physics - conservation of momentum

I'm in my last year of highschool, got a physics question for extra credit that I have no idea how to do. I'm mainly stuck because no numbers are given, obviously it's a conservation of momentum question. I've looked at it for a while but I'm still stumped, any pointers/help is appreciated


Consider the following scenario. You are sitting in a cart containing several bags of sand at the top of a hill. The path you want to take goes down the hill and then up the next, which is higher than yours. There is no friction between your cart and the path. To get started, you throw one bag of sand out the back of the cart. In order to make it as far as possible up the other hill, when should you throw the other bags out? All bags have the same mass and you always throw them at the same speed relative to the cart out of the back.


Edit: So basically because all bags have the same mass and you throw them at the same speed, Delta p for each bag thrown will be the same. Basically to maximize the momentum I have to think about the way that momentum changes if I understand it correctly...we didn't really go over it much in class other than the fact that something called impulse exists, but I don't know how to apply it/if it's even the right thing to apply.

 

How steep is the hill? Youll have to take gravity and force into the calculations as well

 

No numbers are given, the idea is that conservation of energy states the cart would go up to the same height as before, but throwing bags of sand would help climb the steeper hill. I have to figure out (probably using conservation of momentum) when throwing bags of sand would help the most, and then prove it.

 

edit: its already been said, didn't reload page for ages ;-;

 

In all questions we've done so far you're stuck to the track so that's what I'll assume.
Throwing the bags tangent to the curve makes sense, thanks for the thorough explanation. Why does it matter that the bags are thrown out where the curve is flat, vs lets say throwing them out backwards with an angle of 45 degrees downwards if the hill is perfectly inclined at 45 degrees? Both would be throwing the bags tangentially to the curve.

edit: I see what you mean now, these two cases would be the same.

Also if it's at the flattest point (assuming hills that are never flat), the two possibilities are right at the start, and right at the bottom in between the two hills. Would it make a difference where you throw the bags off? Intuition tells me that it shouldn't matter where you throw it off, but one of my friends is telling me that the gravitational potential mgh will be greater at the top of the hill if you decide to throw them off at the bottom of the hill (because of a greater mass), leading to a greater speed.

And another way to think about why throwing it off at the bottom would be better is the fact that kinetic energy is 1/2mv^2, so a change in velocity with a higher velocity (i.e. when the cart is at the bottom) would have a greater overall net effect than when you throw them off right at the top when so much energy is still stored in gravitational potential energy.

 

Thanks a lot guys.