Physics
Physics
Problem
A ball is thrown vertically upward from ground level. Choose the upward direction as positive. (i) Just after being released, at its highest point, and just before returning to the point of projection, state the direction (upward/downward) and sign (positive/negative) of the ball’s linear momentum. (ii) Comment on the correctness of the statement: “The momentum of the ball decreases continuously during its ascent and becomes zero at the top.” Give reasons for your answer without using numerical calculations. (iii) If, instead, the downward direction were taken as positive, how would the signs of the three momenta mentioned in part (i) change? Would any physical prediction about the motion be altered? Explain briefly.Intuitive explanation
Momentum is a vector quantity that depends on both mass and velocity—and velocity includes direction. The key insight is that momentum's sign follows velocity's sign, not the ball's height or speed. At the highest point, velocity is zero (so momentum is zero), but during ascent momentum is negative (moving upward against our positive convention), and it becomes positive only after the ball turns around. Part (ii) tests whether you distinguish between speed (which does decrease then increase) and velocity (which changes continuously and monotonically). Part (iii) explores how choosing a different positive direction flips all signs—but physical predictions remain unchanged because physics doesn't depend on our arbitrary choice of coordinates.
Intuitive explanation
Momentum is a vector quantity that depends on both mass and velocity—and velocity includes direction. The key insight is that momentum's sign follows velocity's sign, not the ball's height or speed. At the highest point, velocity is zero (so momentum is zero), but during ascent momentum is negative (moving upward against our positive convention), and it becomes positive only after the ball turns around. Part (ii) tests whether you distinguish between speed (which does decrease then increase) and velocity (which changes continuously and monotonically). Part (iii) explores how choosing a different positive direction flips all signs—but physical predictions remain unchanged because physics doesn't depend on our arbitrary choice of coordinates.