Step-by-step Answer :
The height from which an object is dropped can be determined using the equation of motion under constant acceleration. In this case, the acceleration is due to gravity (approximately 9.8m/[tex]s^{2}[/tex])
The equation for the height (h) from which an object is dropped is given by:
h = [tex]\frac{1}{2}[/tex][tex]gt^{2}[/tex]
where:
- - h is the height (in meters),
- - g is the acceleration due to gravity (9.8m/[tex]s^{2}[/tex])
- - t is the time the object is in free fall (in seconds).
You mentioned that the ball hits the ground in 2 seconds (t = 2).
h = [tex]\frac{1}{2}[/tex] · (9.8m/[tex]s^{2}[/tex]) · [tex](2s)^{2}[/tex]
h = [tex]\frac{1}{2}[/tex] · (9.8m/[tex]s^{2}[/tex]) · [tex]4s^{2}[/tex]
h = 19.6 m
So, the building must be at least 19.6 meters tall for a dropped ball to hit the ground in 2 seconds, neglecting air resistance.
