Question

You drop a 1.90 kg book to a friend who stands on the ground at distance D = 11.8 m below with outstretched hands at distance d = 1.42 m above the ground.
a)What is the speed of the book when it reaches the hands?
b)If we substituted a second book with twice the mass, what would its speed be?

Answer 1

Assuming we aren't factoring in wind drag or anything like that, the way to solve this is simple. First, find the distance the book falls, which in this case is 11.8-1.42 m, which equals a distance fallen of 10.38 m. Then, we can determine the time it takes for the book to reach your friend by dividing twice the distance fallen (10.38 m) by the force of gravity on Earth (9.8 m/s) and then find the square root, which gives you ~1.455 seconds. Finally, you multiply the force of gravity by the time taken to determine the velocity, which comes out to ~14.26 m/s. And, to answer the second half of the problem, the answer will also be ~14.26 m/s, because mass does not affect acceleration.