Imagine you are on a cart that rests on a frictionless surface (you + car = 100

Question

Imagine you are on a cart that rests on a frictionless surface (you + car = 100 kg) with 30 basketballs (1 kg each). You throw the basketballs off with a speed of 3 m/s relative to the cart every ten seconds. After 5 minutes (when all the basketballs have been thrown), how fast in m/s are you going? You throw the basketballs in the same direction each time. (Hint: Use conservation of linear momentum to find your velocity after a few throws. You should find a pattern and it will become simpler how to determine the answer without much more tedious work.)

Explanation / Answer

Your initial momentum should be equal to your final momentum. Since the cart is initially at rest, the total momentum should always be 0. Just take the sum of the momentums of the cart and 30 basketballs that were thrown out at 3 m/s: 0 = m1*v1 + 30*(m2*v2) Where m1 and v1 are the mass and velocity of the cart, and m2 and v2 are the mass and velocity of each basketball (multiplied by 30 to account for 30 basketballs). You already know m1, m2, and v2, so just solve for v1 and you've got it. To generalize, you can use the formula 0 = m1*v1 + n*(m2*v2) Where n is the number of basketballs that has been thrown.

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