# An earthquake causes a 3 kg book to fall from a shelf. If the book lands with a speed of 4 m/s, from what height did it fall?

##### 1 Answer

#### Explanation:

This can be solved using either kinematics or energy conservation, both methods assuming no outside forces.

**Energy Conservation**

#DeltaE=0#

Where

#U# is the potential energy and#K# is the kinetic energy.

Initially, the book has only gravitational potential energy, as it is stationary above the surface of the earth and

#U_g=K# Where

#U_g=mgh# and#K=1/2mv^2# .

We can solve for

#h=(1/2cancelmv^2)/(cancelmg)#

We are given that

#h=(4m/s)^2/(2*9.8m/s^2)#

#~~0.82m#

**Kinematics**

#v_f^2=v_i^2+2aDeltay#

Because the book begins from rest:

#0=v_i^2+2aDeltay#

Now we solve for

We plug in our values:

**Note** that *acceleration* is equal to