Answer to Question #213370 in Civil and Environmental Engineering for syra

Question

Prove by solution that at the height of 55.86 meters of the Learning Tower of Pisa, Galileo's experiment is true for a 42g baseball and a 46g golf ball to hit the ground at the same time ; thus proving that acceleration due to gravity is constant

Answer 1

Let's understand the Galileo experiment first. He dropped the two balls of different masses simultaneously from the top of the leaning tower of Pisa. Then, he observed that both the balls hit the ground at the same time. This was the Gagikeo experiment. Now, calculate the time to hit the ground of the two different balls that have fallen simultaneously. 

Consider the two balls are dropped with zero initial speed. Use the kinematic equation to find the time of fall.

$s=ut+\frac{1}{2}at^2\\$

here, acceleration due to gravity is the only downward acceleration. Therefore, 

$s=ut+\frac{1}{2}at^2\\ s=ut+gt^2\\ given \space that\\ -s=55.86 m\\ u=0 m/s\\ g=9.8 m/s\\ 55.86 m=0t+gt^2\\ 55.86 m=gt^2\\ t=\sqrt{\frac{55.86}{9.8}}=2.4 s$

It can be observed that there is no dependency of time of fall on the mass of the falling object. 

Therefore, for the same height of 55.86m, the two balls will hit the ground simultaneously.