Question

Jake drops a book out of a window from a height of 10 meters. At what velocity does the book hit the ground?.

Answer 1

Answer: v = 14m/s

Explanation: When jakes drop the book, the book initially only has potential energy (because it is not moving), then the initial energy of the book is E = U = m*g*h

where m is the mass of the book, g is the gravitational acceleration and h is the height.

When the book is almost hitting the ground, for conservation of the energy, the initial potential energy must be transformed into kinetic energy (because at this point we have h = 0 and we lose all our initial potential energy) where kinetic energy is K = (m/2)*v^2

Then we need to solve the next equation for v, that is the velocity:

m*g*h = (m/2)*v^2

v^2 = (2/m)*m*g*h = 2*g*h

v = √(2*g*h)

where g = 9.8m/s^2 and h = 10m

v = (√(2*9.8*10))m/s = 14m/s

So the book hits the ground with a velocity of 14m/s

Answer 2

I think the best way to answer to this kind of question because some of the elements are missing specially the mass of the book is just states the variables and assigned as the mass of an object. So the initial velocity of an object starts at zero and increase rapidly by 9.8 m/s^2 because it is due to gravity