Two objects, position-time graph

[heartofaragorn]

Homework Statement

At t = 0, two objects are thrown from a vertical tower of height H (in m) with an initial speed of v initial (in m/s) in opposite directions (one upwards and one downwards) so that the objects fall to the ground at the base of tower. Ignore the effects of air resistance.

Sketch on the position-time graph below the function s = y up - y down where y up represents the object thrown upward, and y down represents the object thrown downward.

Calculate the difference delta t between the first object hitting the ground and the second.

Homework Equations

y - y initial = +/- v initial x t +1/2

The Attempt at a Solution

I asked my professor about the graph, and he mentioned that the lines should be linear using the equation above, but I'm still confused as to how the graph should look. Also, he said to calculate delta t by using H and other variables listed, but again, I'm just not sure how to accomplish this. Thank you!

 

[Doc Al]

Homework Equations

y - y initial = +/- v initial x t +1/2

That equation is not quite right--the motion is accelerated. Try this:
$$y = y_0 \pm v_0 t - (g/2) t^2$$

where the + is for the object thrown up; the -, for the one thrown down.

The Attempt at a Solution

I asked my professor about the graph, and he mentioned that the lines should be linear using the equation above, but I'm still confused as to how the graph should look.

The graphs would not be linear, but parabolic. (The difference in height between the two objects would be linear.)

 

[heartofaragorn]

Thanks for the help!