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Problem 101 Easy Difficulty

You are standing on a concrete slab that in turn is resting on a frozen lake. Assume there is no friction between the slab and the ice. The slab has a weight five times your weight. If you begin walking forward at 2.00 $\mathrm{m} / \mathrm{s}$ relative to the ice, with what speed, relative to the ice, does the slab move?

Answer

$=-0.400 \mathrm{m} / \mathrm{s}$ in the opposite direction of your motion

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Video Transcript

{'transcript': "problem. Eight points at 93 you're standing on a concrete slab on a frozen lake and as your friend, I have to be honest. I'm getting a little bit concerned about how you keep getting yourself into these situations. But we can have a discussion about that after we do some physics. So you start walking to the right, say, at two meters per second and we want to find out how fast the slab starts going in the opposite direction. It happens to weigh five times as much as you. So this is the center of mass sort of situation, because before you start walking, the center of mass isn't moving. You know that the that has to remain zero, and it also has to be your mass times your speed. Apparently you have two different styles. And why that I can't make up my mind which one I want to use, plus the mass and speed of the slab divided by your total so we can see this is a weighted average of your velocities, which is just the time derivatives of the weighted average of your positions so we can multiply both sides by this and since this zero. It just goes away. Your mass times your speed Is that a pool To negative slabs mass times its speed. So the slab speed is equal? No, it's, you know, speed and direction is equal to your mass provided by its mass. Tend your speed. No, we know that this is 1/5 because this is five times your mass and, uh, no, you know, multiply everything together and we discovered that it's moving a negative zero point or meters per second. Try not to hurt yourself when you fall off the end of it onto the ice. And, uh, this is how fast this will be moving away from you."}