While riding on an elevator descending with a constant speed of 2.7 m/s, you accidentally drop a book from under your arm. How long does it take for the book to reach the elevator floor, 1.0 m below your arm?

0.45 s.

Explanation:

From Newton's equation of motion,

s = ut + 1/2gt² ... Equation 1

Where s = distance, u = initial velocity, a = acceleration, t = time

Given: s = 1.0 m, u = 0 m/s (dropped from height), g = 9.81 m/s²

Substituting into equation 1,

1 = 0 (t) + 1/29.81 (t²)

1 = 9.81t²/2

2 = 9.81t²

t² = 2/9.81

t² = 0.204

t = √ (0.204)

t = 0.45 s.

Hence it takes 0.45 s for the book to reach the elevator floor.