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)`