Aball thrown vertically upward is caught by the thrower after 2.00 s. find (a) the initial velocity of the ball and (b) the maximum height the ball reaches.

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:

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)  

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:

15.3 cos 65 degrees trig