A tennis coach launches practice balls vertically upward from a machine positioned at…
PHYSICS · Multi-part · CBSE · Physics · Motion in a Straight Line · Motion in a Straight Line
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.