Question

in the middle of science class, you have a great idea. being on the fourth floor, you get a friend to watch out the window of the third, second and first floors just beneath you. you have all your friends on a conference call on your cell phone and tell them to let you know when they see a book you drop out your window pass by their window. which statement is true of the amount of time it takes to pass by each window?
a the time interval between floors is the same
b the time interval between floors becomes less each time
c the time interval between floors becomes more each time
d the time interval between floors becomes infinitely long

Explanation:

The problem involves the motion of a dropped book, which is a free - fall motion (a type of uniformly accelerated motion, with acceleration due to gravity \(g\)). In free - fall, the distance fallen \(d = v_0t+\frac{1}{2}gt^{2}\), and the velocity \(v = v_0+gt\) (where \(v_0 = 0\) for a dropped object). As the book falls, its velocity is constantly increasing. The distance between consecutive floors is the same (assuming uniform floor spacing). The time taken to cover a distance \(d\) with an initial velocity \(v_{i}\) and acceleration \(g\) is given by \(d=v_{i}t+\frac{1}{2}gt^{2}\). As the book moves from a higher floor to a lower floor, its initial velocity for each subsequent floor - to - floor interval is higher. For a fixed distance \(d\) (between floors), when the initial velocity \(v_{i}\) is higher, the time \(t\) taken to cover that distance will be less. So the time interval between floors becomes less each time.

Answer:

B. the time interval between floors becomes less each time