Question

You drop a 2.00 kg book to a friend who stands on the ground at distance D = 12.0 m below. Your friend's outstretched hands are at distance d = 1.80 m above the ground (see the figure). (a) What is the speed of the book when it reaches her hands? (b) If we substituted a second book with twice the mass, what would its speed be when it reaches her hands? (c) If, instead, the book were thrown down with initial speed 5.00 m/s, what would be the answer to (a)?

Answer 1

Given information is

mass of the book = 2 kg

actual distance the book covered is D-d= 12-1.8 = 10.2m

considering free fall (motion with uniform acceleration) of a book, book will experience the downward acceleration g = 9.8 m/s²

the kinematic equation that describes the object motion are given by,

here, d = displacement

        = initial velocity

        = final velocity

        t = time

        a = acceleration

(a) What is the speed of book when it reaches your friends hands?

we will use the kinematic equation

here = 0 m/s

      a = -9.8 m/s² (acceleration due to gravity)

      d = 10.2 m (since the actual distance covered by book is 12 - 1.8 = 10.2 m)

Putting all these values in equation, we get

(b) If we substitute the second book with twice mass then speed will not be changed. since mass of the object doesn't affect the time taken for it to fall.

so 4 kg book will take same time to reach your friends hand as the 2 kg book will take.

(c) initial velocity of book