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?
Answers
Answer:
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} }V
R
=
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}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
Given:
A book is pushed with an initial horizontal velocity of 5.0 m/s off the top of a desk.
To find:
Initial vertical velocity?
Calculation:
As the book get horizontally thrown off from the top of the desk, we can this to be a "Air - Ground" Projectile.
- Now, see the diagram.
At the point of projection from the edge of the table, the horizontal component of velocity of the book is 5 m/s.
However, the vertical component of the velocity will be 0 m/s.
- Please note that : acceleration due to gravity will only work on the vertical component of velocity and not on the horizontal component.
Hope It Helps.
