You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity

v
at an angle θ with respect to the horizontal. Let the building be 49.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 11.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released.

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