You have a mass of 70 kg. You are sitting on a 14-kg sled, which can slide across the surface of a frozen pond (which is horizontal and frictionless). You have five heavy rocks (7 kg each) with you in the sled. You are going to attempt to propel the sled forward by throwing these rocks out the back of the sled. If the sled starts at rest, and you can throw the rocks at a speed of 8 m/s relative to the sled, how fast will the sled be traveling after you have thrown all five rocks?

Apply the principle of conservation of momentumn. Please show us your attempt at solving this, and we'll help if you get stuck.

so would I use m1v1=m2v2? So v1=(m2/m1)v2, then v1=(84kg / 35kg)*40 m/s which = 3.3 m/s?

Couple of issues:

1. Be carfeul how you define and use m1, v1, m2, and v2. It seems you set v1 as the velocity of the sled, by then used the mass of the rocks for m1, whereas the mass of the sled + rider + rocks being carried should be m1, and the mass of one rock is m2..

2. Where did the 40 m/s come from? The velocity of each rock throw is 8 m/s. And also (84/35)*40 does not equal 3.3.

3. The value for m1 is not 84 Kg - remember that the rocks must be included as well! So for the first throw m1 = 70 + 14 + 4x7, for the second throw m1 = 70+14 + 3 x 7, etc. You're going to have to calculate the change in velocity of m1 for each of the 5 throws of a rock and then add them up to get the total v1.

so should I end up with a formula like this, Vs=(MrVr/Ms1) + (MrVr/Ms2) + (MrVr/Ms3) + (MrVr/Ms4) + (MrVr/Ms5)? If so would the answer be 2.89 m/s?

Yes - that is correct! Now you're going to have to change your name to "physicsrocks99"

Thank you very much for the help! And I sure am haha