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6. At time `t = 0`, a student throws a set of keys vertically upward to her sorority sister, who is in a window at distance `h` above. The second student catches the keys at time `t`.
(a) With what initial velocity were the keys thrown?
(b) What was the velocity of the keys just before they were caught?
`v_f = v_i + at`; `x_f = x_i + v_it + 1/2 at^2`
(a) `h/t + 4.90t`
(b)`h/t - 4.90t`
Givens:
`t`
`y_i=0`
`y_f = h`
`a = -g = 9.80 m//s^2`
(a)
`y_f = y_i + v_it + 1/2 at^2`
`=>h = 0 + v_it -4.90t^2`
`=> v_i = (h-0 + 4.90t^2)/t`
`=> v_i = color(red)(h/t + 4.90t)`
(b)
`v_f = v_i + at`
`v_f = h/t + 4.90t +(-9.80)t = color(red)(h/t - 4.90t)`
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