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Projectile Motion with Horizontal Acceleration

We did a problem that involved a projectile motion situation where an electrostatic force meant that there was a horizontal acceleration and a gravitational force meant that there was a vertical one. (See for example 1998 AP Physics B № 2.)

 

Unlike the projectile motion problems we're used to, where the object follows a parabolic path, when there's constant acceleration in both dimensions it seems to follow a linear path. We can break down two dimensional motion into horizontal and vertical motion diagrams, as seen here (To see this produced in real time, I highly recommend PSSC's Free Fall and Projectile Motion, www.youtube.com/watch?v=QRa_Eh9mv9Y, from 11:50 to 13:56)

 

Because in both dimensions position has a quadratic time dependence when there's horizontal acceleration, the resultant position in two dimensions changes linearly rather than parabolically.

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Uploaded on November 7, 2019
Taken on November 7, 2019