and 
. Verify that the following graph correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take 
. Give the equations for the linear and curved parts of the plot.
Fig. 3.95
Answer:
If we take origin for position measurement on the ground, then the positions of the two stones at any instant will be
...(1)
...(2)
When the first stone hits the ground,
or 
or 
or 
As time cannot be negative, so t = 8 s
i.e. the first stone hits the ground after 8 s.
From (1) and (2), the relative position of second stone w.r.t. first is given by
As there is a linear relationship between 
and t, so the graph is straight line OA up to t = 8 s. After t = 8 s, only the second stone is in motion. So the graph is parabolic (AB) in accordance with quadratic equation,
The second stone will hit the ground, when 
or 
On solving, t = 10 s
After t = 10 s, the separation between the balls is zero, which explains the part BC of the graph.
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