Dennis drops a quarter from a skyscraper with floors spaced 3 m apart. If the quarter hits the ground at 25 m/s, how many floors above ground is Dennis?

Question

Dennis drops a quarter from a skyscraper with floors spaced 3 m apart. If the quarter hits the ground at 25 m/s, how many floors above ground is Dennis? Ignore air drag.

Answer 1

Let

d = 3 m be the spacing between floors,

v = 25 m/s be the final speed,

g = 9.8 m/s² be gravitational acceleration,

h (to be calculated) be the height of Dennis's position,

t (unknown) be the time the quarter falls.

From definition of acceleration follow these equations

v = gt

h = gt²/2

Therefore

t = v/g

h = g(v/g)²/2 = v²/2g

Substituting actual numbers

h = 25² m²/s² / (2 x 9.8 m/s²) = 31.9 m

That is more than 10 floors.