AP Physics C 1.1 Newtonian Mechanics
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AP Physics C: Newtonian Mechanics Drill 1, Problem 1. Which of Newton's equations of motion would have to be modified to account for the airplane's uniform speed of 220 meters per second?
|AP Physics B||Newtonian Mechanics|
|AP Physics B/C||Newtonian Mechanics|
|AP Physics C||Newtonian Mechanics|
If she had launched some food and wanted to estimate the launch angle required to hit
a target, which of Newton's equations of motion would
have to be modified to account for the airplane's uniform speed of 220 meters per second?
Initial and final velocities are u and v respectively, d is displacement, a is acceleration,
and t is time.
And here are the potential answers...
This problem might be intimidating at first... but before diving right into the answer choices,
let's think about the bigger picture here.
Ok. A high school student is on a plane, and is thinking about physics.
What's wrong with this picture? It's already amazing.
Specifically, she's thinking about the physics of launching some of her less than palatable
food across the aisle to hit her victim.
But we're told the plane is moving forward at a rate of 220 meters per second.
How do we account for this movement, to ensure that the victim, and only the victim gets
beaned by... beans?
Well this problem is actually testing us on our ability to isolate systems.
In other words, we have to determine whether or not the airplane's movement actually affects
the food projectile's flight, and the answer is....no.
Because the girl is sitting in the plane, which is moving at 220 meters per second,
the girl is also moving at 220 meters per second.
Boy, she's speedy.
And oh by the way, the beans are moving at 220 meters per second too.
Because her launching food takes place all in the plane, it means that the catapult and
her projectile, before she fires it, is also moving at 220 meters per second.
Keep in mind that all this "movement" is relative to the earth.
If we think about the airplane as an isolated system, with the girl, her weapons of destruction,
and her victim all contained inside the system...
...we can see that they are all stationary relative to each other because they are all
moving at 220 meters per second.
If this doesn't make sense, think about people on earth.
Every moment, we are rotating around the earth's axis at 1000 miles an hour,
around the sun at around 67,000 miles an hour,
and around our galaxy at 483,000 miles an hour.
We don't feel a thing because we're always moving this fast relative to space...
and everyone else, but relative to the earth, we aren't moving at all...
It's a good thing too, since we'd find it tough to play baseball if the balls couldn't
keep up with the earth.
With all this said, we can come full circle and answer the question.
Since the airplane is an isolated system, the movement of the airplane doesn't affect
the trajectory of the projectile.
The answer is (E), we don't have to modify any of the basic kinematics equations to accommodate
for the airplane's movement.
Well hey, sounds like the stars are aligned... heads up in Seat 17F...