What is the speed at which the object was thrown upward?

[jgens]

Homework Statement

You throw an object directly upward at the same time a person drops an object down to you from a height, H. The two objects pass at a height H/2. With what speed did you throw the object upward?

Homework Equations

Simple kinematics equations.

The Attempt at a Solution

I haven't done physics for a while so I'm not certain if I'm entirely off track on this one:

I set up two equations for the motion of the balls (I'm allowing g = -10m/s/s); hence, I got h_a = (gt^2)/2 + H and h_b = (gt^2)/2 + vbi(t) where h_a is the height of the ball being dropped and h_b is the height of the ball being thrown (sorry if my notation is poor or non-standard). Since the balls are released simultaneously and pass at height H/2, I allow t1 to designate the amount of time required for the balls to reach H/2. By equating the two (h_a = h_b = H/2) I get (gt1^2)/2 + H = (gt1^2)/2 + vbi(t1), which solving for vbi produces vbi = H/t1. To solve for t1 I set up the equation H/2 = (gt1^2)/2 + H, and with some manipulations get t1^2 = -H/g and consequently t1 = sqrt(H/abs(g)). Using my value for t1 in my equation for vbi yields vbi = H(sqrt(abs(g)/H) = sqrt(Habs(g)).

Sorry the work is so messy, I don't know how to use Latex.

 

[Delphi51]

Looks good to me! Nicely done.

 

[jgens]

Thanks!