Question

A book is pushed with an initial horizontal velocity of 5.0 meters per second off the top of a desk. What is the initial vertical velocity of the book, in m/s?

Answer 1

Answer:

The Initial vertical velocity is zero

Explanation:

Given that,

A book is pushed with an initial horizontal velocity, Vx = 5 m/s

According to projectile motion, the horizontal component of velocity i.e., in X-axis remains the same though out its path.

The vertical velocity varies i.e., the velocity towards the Y- axis.

The velocity of the falling book in its trajectory is the resultant velocity. Due to the action of gravity, it keeps on increasing with time.

The resultant velocity is given by relation

                $V_{R} = \sqrt{{V_{x}^{2}} +[ {gt}]^{2} }$

where

               gt = Vy - vertical velocity

                        g - acceleration due to gravity

                        t - time

Since, the initial horizontal velocity at that instant is equal to the resultant velocity.

                  Vx  = 5 m/s

                  $V_{R}$  = 5   m/s

So, on substituting in the above equation          

                         Vy = 0  m/s

Therefore, the initial vertical velocity is equal to zero