How long would it take for two rocks to hit the ground from 177 feet in the air?

Question

According to the legend, in 1589 the Italian scientist Galileo Galilei dropped two rocks of different weights from the top of Leaning tower of Pisa. He wanted to show that the rocks would hit the ground at the same time. Given that the tower's height is about 177 feet, how long would it have taken for the rocks to hit the ground?

Answer 1

h(t) = -16t² + v₀t + h₀

 

We are solving for t when height is 0

 

v₀ = 0; no initial velocity

 

h₀ = 177;  initial height was 177 feet

 

             0 = -16t² + 177

 

        -177 = -16t²

 

(-177/-16) = t²

 

       3.326 = t

 

It would take 3.326 seconds for the rocks to hit the ground