an egg is dropped from the top of the library roof. then 2.2 seconds after that a second egg is thrown straight down with an initial speed of 58m/s. it is then observed that the two eggs splat on the ground at the same instant. how high in meters is the library

39.8 m

Explanation:

Let h be the required height and t be the time to reach the egg which was thrown later on. The egg thrown earlier took (t + 2.2) s, with initial velocity zero to cover distance of h.,

So

h = 1/2 g (t + 2.2) ²

For the egg thrown with velocity of 58 m/s

h = 58 t + 1/2 g t²

Equating these two equations

1/2 g (t + 2.2) ² = 58 t + 1/2 g t²

1/2 g (t² + 4.4 t + 4.84) = 58 t + 1/2 g t²

58 t = 21.56 t + 23.716

t =.65 s

h = 1/2 x 9.8 x (2.2+.65) ²

h = 39.8 m