Answer:
A parabolic curve (concave down), represents the best graph that depicts the time variation of relative position of the second stone with respect to the first.
Step-by-step explanation:
To find the graph that best represents the time variation of relative position of the second stone with respect to the first, we need to consider the motion of both stones. Let's analyze their motion separately and then find the relative position between them at different times.
We can use the following kinematic equations to describe the motion of each stone:
For stone 1 (initial speed = 10 m/s):
Initial height (h) = 240 m
Initial velocity (u) = 10 m/s (upwards, since it's thrown up)
Acceleration (a) = -10 m/s² (negative because it's acting against the direction of motion)
Final velocity (v) = 0 m/s (at the highest point, the velocity becomes 0)
The equation for the height (y) of stone 1 at time (t) is given by:
y₁(t) = h + ut + (1/2)at²
For stone 2 (initial speed = 40 m/s):
Initial height (h) = 240 m
Initial velocity (u) = 40 m/s (upwards, since it's thrown up)
Acceleration (a) = -10 m/s² (same as stone 1, as gravity acts the same on both stones)
Final velocity (v) = 0 m/s (at the highest point, the velocity becomes 0)
The equation for the height (y) of stone 2 at time (t) is given by:
y₂(t) = h + ut + (1/2)at²
To find the relative position of stone 2 with respect to stone 1 at time (t), we subtract the height of stone 1 from the height of stone 2:
Relative position (R) = y₂(t) - y₁(t)
Now let's plot the relative position on the y-axis against time on the x-axis for different times (t).
Since it's a multiple-choice question, let's look at the options and analyze them one by one:
Option A: Linearly increasing graph with time:
This option would represent constant relative velocity between the stones, which is not the case. The relative position should change as the stones have different initial velocities.
Option B: Linearly decreasing graph with time:
This option would represent the relative position decreasing at a constant rate, which is also not the case. The stones are thrown upwards, so their relative position won't decrease at a constant rate.
Option C: Parabolic curve (concave down):
This option seems reasonable since both stones are moving upwards initially and then they will come down. The relative position will increase, reach a maximum when the stones are at their highest points, and then decrease again.
Option D: Parabolic curve (concave up):
This option is not plausible. The relative position won't increase at an increasing rate as time goes on.
Considering the analysis above, Option C, a parabolic curve (concave down), represents the best graph that depicts the time variation of relative position of the second stone with respect to the first.