ShmoopTube

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Here's your shmoop du jour, brought to you by Airplanes.

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In the event of an emergency, your Physics textbook MAY be used as a flotation device.

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A high-school student on a long plane journey thinks about doing a projectile experiment

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using some of the airplane food... just from a spoon, not her stomach...but her

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better judgment takes over and she refrains.

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If she had launched some food and wanted to estimate the launch angle required to hit

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a target, which of Newton's equations of motion would

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have to be modified to account for the airplane's uniform speed of 220 meters per second?

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Initial and final velocities are u and v respectively, d is displacement, a is acceleration,

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and t is time.

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And here are the potential answers...

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This problem might be intimidating at first... but before diving right into the answer choices,

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let's think about the bigger picture here.

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Ok. A high school student is on a plane, and is thinking about physics.

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What's wrong with this picture? It's already amazing.

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Specifically, she's thinking about the physics of launching some of her less than palatable

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food across the aisle to hit her victim.

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But we're told the plane is moving forward at a rate of 220 meters per second.

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How do we account for this movement, to ensure that the victim, and only the victim gets

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beaned by... beans?

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Well this problem is actually testing us on our ability to isolate systems.

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In other words, we have to determine whether or not the airplane's movement actually affects

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the food projectile's flight, and the answer is....no.

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Because the girl is sitting in the plane, which is moving at 220 meters per second,

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the girl is also moving at 220 meters per second.

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Boy, she's speedy.

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And oh by the way, the beans are moving at 220 meters per second too.

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Because her launching food takes place all in the plane, it means that the catapult and

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her projectile, before she fires it, is also moving at 220 meters per second.

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Keep in mind that all this "movement" is relative to the earth.

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If we think about the airplane as an isolated system, with the girl, her weapons of destruction,

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and her victim all contained inside the system...

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...we can see that they are all stationary relative to each other because they are all

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moving at 220 meters per second.

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If this doesn't make sense, think about people on earth.

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Every moment, we are rotating around the earth's axis at 1000 miles an hour,

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around the sun at around 67,000 miles an hour,

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and around our galaxy at 483,000 miles an hour.

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That's.... fast.

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We don't feel a thing because we're always moving this fast relative to space...

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and everyone else, but relative to the earth, we aren't moving at all...

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It's a good thing too, since we'd find it tough to play baseball if the balls couldn't

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keep up with the earth.

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With all this said, we can come full circle and answer the question.

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Since the airplane is an isolated system, the movement of the airplane doesn't affect

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the trajectory of the projectile.

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The answer is (E), we don't have to modify any of the basic kinematics equations to accommodate

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for the airplane's movement.

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Well hey, sounds like the stars are aligned... heads up in Seat 17F...

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