Question

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

Answer 1

39.8 m

Step-by-step 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