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In this problem, we have raindrops falling vertically relative to the earth, and we have a car moving to the east at a speed of 40 kilometers per hour.
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The goal of the problem is to get the relative velocity of the raindrop relative to the car and relative to the earth.
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Now, notation.
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D, g.
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This is the velocity of the drop relative to the ground, the earth.
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I've chosen g just for readability.
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Earth, same thing.
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So velocity of the drop relative to the ground, relative velocity of the car, relative to the ground.
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So that's my notation.
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Now, this is actually relative motion problem, two -dimensional relative motion problem.
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And what's a good visualization to give us the idea what to do here? think of a person moving on a boat and that boat is moving relative to the shore.
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And we want the velocity of the person relative to the shore.
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How do you do it? well, you take the velocity of the person relative to the boat, add to that as a vector velocity of the boat, relative to the shore.
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And you got what the person doing relative to the shore.
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So vector operation, vector sum.
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So using that idea here, the drop relative to the ground is equal to the drop relative to the car plus the car relative to the ground.
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As vectors.
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So vector sum.
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So there's that idea put together.
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Notice something.
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The c appear side by side.
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So if you think of dropping them off, crossing them off, d followed by a g.
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That's the same as what's on the left.
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That's how you can keep track of what you want on the left that you're going to get from, that you have the right sum on the right hand side.
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So this means a vd, is the resultant, the sum of these two vectors.
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So let's see what we have to get.
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So our second vector is cg.
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Now let's remember the triangle rule.
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Triangle will we draw from the tail of the first to the tip of the second.
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So here is going to be the resultant, dg.
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He's drawn from the tail of the first to the tip of the second.
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This is vcg.
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So all we got to do is fill in the first vector.
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Vdc.
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But we know this is the tail of vdc, and this is going to be the tip of vdc.
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So there is our triangle rule.
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Let me go through the triangle rule again.
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We put the tail of the second vector at the tip of the first.
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So we have that.
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Then we draw from the tail of the first to the tip of the second...