The initial velocity of the keys is 13.17 m/s.
A student tosses her sorority sister, who is in a window 2.30 meters above, a set of keys vertically upward.
The second student catches the key 2.50s later.
We simulate the keys as a particle falling at a steady speed. Assume that the positions of the first and second students are, respectively, y(i) = 0 and y(f) = 2.30m.
Now, we have
The time of flight of the keys is t = 2.50 seconds.
Now, the acceleration is a(y) = -9.8 m/s²
We will use the equation of motion,
y(f) = y(i) + v(yi) × t + ( 1/2 ) × a(y) × t²
v(yi) = [ y(f) - y(i) - ( 1/2 ) × a(y) × t² ] / t
v(yi) = [ 2.3 - 0 - ( 1/2 ) × ( - 9.8 ) × (2.5)² ] / 2.50
v(yi) = [ 2.3 + 30.625 ] / 2.50
v(yi) = 32.925 / 2.5
v(yi) = 13.17 m/s
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