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

$y=78.4\,\mathrm m-\dfrac12gt^2$

where $g=9.80\,\frac{\mathrm m}{\mathrm s}$. It reaches the ground when $y=0$, at a time $t$ such that

$0=78.4\,\mathrm m-\dfrac12gt^2\implies t=4.00\,\mathrm s$

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.