Answer:
a) 9.8 m/s
b) 4.9 m
Explanation:
This problem is a good example of Vertical motion, where the main equations for this situation are:
(1)
(2)
Where:
is the height of the ball at a given time
is the initial height of the ball (assuming the hand of the thrower the origin of the system)
is the initial velocity of the ball
is the final velocity of the ball
is the time it takes for the ball to make the complete movement (from the moment it is thrown until it falls back into the pitcher's hands)
is the acceleration due to gravity
Knowing this, let's begin with the answers:
<h3>a) Initial velocity
</h3>
In order to find the initial velocity of the ball, we will use equation (1) and , taking into account that 
and at this given time:
(3)
Isolating :
(4)
(5)
Then:
(6)
<h3>b) Maximum height
</h3>
In this part, we will use equation (2), knowing the value of the height is maximum when 
. So, we will name this height as 
:
(7)
Isolating :
(8)
(9)
Finally:
