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## Homework Statement

A student throws a set of keys vertically upward to her sorority sister, who is in a window 2.00 m above. The second student catches the keys 2.30 s later.

(a) What was the velocity of the keys just before they were caught?

I did y(t) = 2 - 4.9t² + v₀t

2 = 0 - 4.9(2.3)² + v₀(2.3)

v₀ = 12.1m/s

Now I have two formulas, v² = v₀² + 2ad and v = v₀ + at, but they give me different answers.

v² = v₀² + 2ad

v² = (12.1)² + 2(-9.8)(2)

v² = 107.21

v = 10.4m/s

v = v₀ + at

v = 12.1 - 9.8(2.3)

v = -10.4m/s

I understand the square root will give us a negative as well, but the question is, HOW DO WE KNOW which to take? I hadn't use the v = v₀ + at, I wouldn't know whether to take positive or negative.