Vertical Motion w/ constant acceleration

AI Thread Summary
To solve the problem of two balls hitting the ground simultaneously, one thrown upwards and the other dropped, it's essential to use the equations of motion for constant acceleration. The key is that both balls must have the same total time of flight, despite the first ball being thrown 1.14 seconds earlier. The equations vf^2 = v0^2 + 2ax and x = x0 + v0t + 1/2at^2 are relevant for determining the initial speed of the first ball. The confusion arises from having two unknowns, but focusing on the time variable can help clarify the relationship between the two motions. Properly applying these equations will yield the initial speed needed for the first ball to ensure both hit the ground at the same time.
cdlegendary
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Homework Statement



A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of 1.14 s later. You may ignore air resistance.

A.) If the height of the building is 20.6 m, what must the initial speed be of the first ball if both are to hit the ground at the same time?

Homework Equations



vf^2 = v0^2 + 2ax
vf = v0 + at
x = x0 + v0t + 1/2at^2

The Attempt at a Solution



I'm really not sure where to start. If someone could help me out I would greatly appreciate it.
 
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Focus on the last of your three equations. "t" has to be the same for both objects: the one that's dropped, and the one that's thrown up.
 
ideasrule said:
Focus on the last of your three equations. "t" has to be the same for both objects: the one that's dropped, and the one that's thrown up.

Hmm but wouldn't there be two unknowns for that equation? I tried setting the equation equal to itsel but it turned out kind of badly, haha...
 

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