A small rubber ball is released from rest from a balcony 2.0 m above a horizontal sidewalk. A strobe photograph is taken, producing images every 0.050 s.
• Between release and first contact with the sidewalk, the vertical spacing between successive images increases.
• During contact with the sidewalk the ball remains in contact for 0.040 s, and during that interval only two nearly overlapping images appear.
• After the bounce the ball rises, the vertical spacing between successive images decreases, and the ball reaches a maximum height of 1.20 m above the sidewalk before it begins to fall again.
Consider only the interval that begins with the release of the ball and ends the instant it reaches the 1.20 m maximum height after rebounding.
(a) On axes in your response booklet, draw a clearly labeled, qualitative position–time graph for the ball over the described interval. Indicate and label the instant of sidewalk contact and every instant at which the ball’s velocity is zero.
(b) Using the graph from part (a) as a guide, sketch a velocity–time graph for the same interval on a separate set of axes. Clearly label when the ball is in contact with the sidewalk and when its velocity is zero.
(c) Just before hitting the sidewalk, the ball’s speed is 6.0 m/s downward. At the instant it leaves the sidewalk, its speed is 4.8 m/s upward. Using these values and the contact time given in the stimulus, determine the ball’s average vertical acceleration while it is in contact with the sidewalk. Show your reasoning and include appropriate units.
(d) Explain whether the velocity–time graph you drew in part (b) is consistent with the ball reaching the stated 1.20 m rebound height. Refer specifically to features of your graph in your explanation.