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Gettin' shmoopy with it...

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You are carefully carrying your father's 15 kilogram bowling ball across a muddy field when you drop it.

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Heaven only knows where you were going with it. If it falls 1 meter, and the ball sinks into

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the mud to a depth of 10 centimeters, what is the magnitude of the constant acceleration

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due to the mud? And here are the possible answers...

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First of all, that's a heavy bowling ball, and you're lucky it didn't fall on your feet.

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Now, onto physics. This problem takes place in two parts.

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First, you drop the ball, and it falls to the mud below.

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Then, once it lands, the mud pushes back on the bowling ball, and stops it.

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Let's start by looking at the falling portion of this problem.

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When the bowling ball first begins to drop, it's in free-fall, and it follows all of

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the rules associated with free-fall. Like... waving its arms over its head and screaming.

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Remember that in kinematics, we have a few key terms:

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Displacement is the distance between an object and its original location.

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Velocity is the speed of the object in a particular direction.

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We find velocity by dividing the

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object's displacement by the time it took for it to move that far.

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Finally, acceleration is how fast the object is changing its velocity.

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In this problem, initial velocity is 0, starting displacement is 0 meters, final displacement

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is 1 meter, acceleration is 10 meters per second squared, and the time is... irrelevant.

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For this problem, anyway. The final velocity, which is left over, is

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what we're trying to find. To do that, we call upon the power of our

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kinematics equations. In particular, v sub f squared equals nought squared plus 2a times

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the quantity x sub f minus x sub zero. Since v nought and X nought = 0 we can make

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those terms go away, and only worry about v sub f, A, and x sub f.

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We can plug in the values we know for a and x, or we could substitute in variables.

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If we went the latter route, we would find that sub f squared equals 2gh, where g is

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equal to the acceleration due to gravity or 10 meters per second squared, and h is the

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height the bowling ball will fall.

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Taking the square root of both sides,

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we get that v sub f equals the square root of 2ax sub f.

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Phew, that was exhausting, and we're only half done.

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Fight through the pain.

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Once the ball finishes dropping, it begins

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slowing down because of the mud. The final velocity will be 0, because the

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ball has stopped moving. Again, we assume that the beginning of the ball's movement

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is displacement = 0, and the final is .1 meters, because the ball sinks in .1 meters.

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Time is again, irrelevant, but we're missing both acceleration and initial velocity.

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But wait! In the first part, we found out what the initial velocity was. It's √2gh.

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Great. Now, just like in the first part, we take the equation v sub f squared = v nought

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squared + 2a times the quantity x sub f minus x nought... and plug in what we know.

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If we left out the actual values of g and h, now is the time to plug them in.

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Now's the hard part. We have to do Algebra. Wince.

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First we do all of the multiplication we can, and get 20 plus .2a is equal to 0.

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Next, we move the 20 over to the other side of the equation by subtracting,

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and finally, divide by .2.

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Our answer is negative, and none of the answer

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choices are negative. Did we make a mistake? Actually, we didn't.

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In physics, negative signs usually indicate direction. For example, if moving to the right

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was positive displacement, then a negative value would be moving to the left.

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In this case, the negative values just mean that the acceleration is opposite our velocity,

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which was downwards. If we think of up as positive, then our answer

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would be 100 meters per second squared... ...or answer D.

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Of course, none of this really matters... since your dad's gonna kill you when he

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finds out you took his nice bowling ball.

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