Question

You and your friend are on the roof of a 20 m tall building investigating a free fall. Your friend releases a small rock from rest. You throw another rock simultaneously with your friend aiming it straight down.
(a) What initial speed should you supply to the rock so it hits the ground one second before the friend's one? Use g = 10 m/s^2.

Answer 1

time for first rock
-20 = -5 t^2
t = 2 seconds to fall

so t for second ball = 2 - 1 = 1 second
-20 = -Vi t + -5 t^2
20 = -Vi + 5
Vi = -15 m/s (the - sign means speed is down)