## Related questions with answers

A hard rubber ball, not affected by air resistance in its motion, is tossed upward from shoulder height, falls to the sidewalk, rebounds to a somewhat smaller maximum height, and is caught on its way down again. This motion is represented where the successive positions of the ball (A) through (G) are not equally spaced in time. At point (E) the center of the ball is at its lowest point in the motion. The motion of the ball is along a straight line, but the diagram shows successive positions offset to the right to avoid overlapping. Choose the positive $y$ direction to be upward.

($i$) Rank the situations (A) through (G) according to the speed of the ball $\left|v_y\right|$ at each point, with the largest speed first.

($ii$) Rank the same situations according to the velocity of the ball at each point.

($iii$) Rank the same situations according to the acceleration $a_y$ of the ball at each point. In each ranking, remember that zero is greater than a negative value. If two values are equal, show that they are equal in your ranking.

Solution

Verified- At point B, when ball gets its maximum height its velocity will be 0 and it will start to accelerate downwards, same when it reaches point E and hits sidewalk. So both of velocities in one moment will be 0. In this case we have $v_b=v_e$
- At point D ball will have maximum velocity, since it is just about to hit the sidewalk from 'free' fall.
- At points A and C it will have the same velocity since ball lost its velocity to reach maximum under the influence of gravity, and on other side, after reaching maximum height, gravity will accelerate it downwards and at point C velocity will be the same as in point A.So we have: $v_a=v_c$
- At point F ball will have smaller velocity because energy is lost since impact wasn't elastic.
- At point G, ball will have smaller velocity since, again, ball lost some energy on impact, and its velocity can't be the same as at point C.

In this case, ranking from largest to smallest velocities will be:

$D>F>A=C>G>B=E$

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