Question

galileo dropped a cannonball and a lightweight ball off of the leaning tower of pisa from the same height at the same time to illustrate the effect of gravity. assume there was no wind that day. describe what happened as the objects hit the ground. they hit at the same time. why?

Explanation:

Step1: Recall gravity - related principle

In the absence of air - resistance (no wind means no air - resistance here), all objects in free - fall near the Earth's surface experience the same acceleration due to gravity, approximately $g = 9.8\ m/s^{2}$.

Step2: Apply kinematic equation

The kinematic equation for vertical motion is $h=v_{0}t+\frac{1}{2}gt^{2}$. Since the objects are dropped ($v_{0} = 0$) from the same height $h$, and $h=\frac{1}{2}gt^{2}$, solving for $t$ gives $t=\sqrt{\frac{2h}{g}}$. Since $h$ and $g$ are the same for both objects, the time $t$ it takes for them to reach the ground is the same.

Answer:

They hit at the same time because in the absence of air - resistance, all objects in free - fall near the Earth's surface have the same acceleration due to gravity and fall from the same height in the same time according to the kinematic equations of motion.