Question

A physics book is thrown horizontally at a velocity of 5.0 m/s from the top of a cliff 78.4 m high. How long does the book take to reach the bottom of the cliff .

Answer 1

The book's vertical position in the air is

`y=78.4\,\mathrm m-\frac12gt^2`

where
`g=9.80\,(\mathrm m)/(\mathrm s)`. It reaches the ground when
`y=0`, at a time
`t` such that

`0=78.4\,\mathrm m-\frac12gt^2\implies t=4.00\,\mathrm s`

So it takes the book 4 seconds to reach the bottom. The given initial velocity is irrelevant since it only has a horizontal component; vertically, the book is starting from rest.