Physics
Physics
Problem
A tennis coach launches practice balls vertically upward from a machine positioned at ground level. The acceleration due to gravity is constant and downward. For several balls, the coach uses the same numerical values for initial speed and release height, but she sometimes chooses the positive direction to be upward and other times chooses it to be downward when performing her written calculations. Answer the following questions about how the choice of coordinate system affects the algebraic representation of the motion while leaving the underlying physics unchanged. (a) Describe, in words, how assigning the upward direction to be positive versus assigning the downward direction to be positive determines the algebraic sign of each of the following quantities during the ball’s flight: displacement from the launch point, instantaneous velocity, and acceleration due to gravity. (b) For the upward-positive convention, state whether each quantity in part (a) is positive, negative, or zero during (i) the ascent, (ii) the highest point, and (iii) the descent. Justify each answer verbally rather than by using numerical values. (c) Explain how a single kinematic equation that contains displacement, initial velocity, acceleration, and time can correctly predict the ball’s position at any instant provided that all quantities are substituted with signs consistent with the chosen coordinate system.Intuitive explanation
The key insight is that choosing a coordinate direction is purely a bookkeeping choice—it changes the signs of your equations but never the physical outcome. When you flip from "up is positive" to "down is positive," initial velocity, acceleration, and displacement all flip their signs together in a way that keeps your final answers (like time in air or maximum height) identical. Understanding this teaches you that physics is coordinate-independent: the math is just a tool we adapt to our convenience, not a reflection of reality itself.
Intuitive explanation
The key insight is that choosing a coordinate direction is purely a bookkeeping choice—it changes the signs of your equations but never the physical outcome. When you flip from "up is positive" to "down is positive," initial velocity, acceleration, and displacement all flip their signs together in a way that keeps your final answers (like time in air or maximum height) identical. Understanding this teaches you that physics is coordinate-independent: the math is just a tool we adapt to our convenience, not a reflection of reality itself.