Watching the World Series (only as an example of physics in action), you wonder about the ability of the catcher to throw out a base runner trying to steal second. Suppose a catcher is crouched down behind the plate when he observes the runner breaking for second. After he gets the ball from the pitcher, he throws as hard as necessary to second base without standing up. If the catcher throws the ball at an angle of 30 degrees from the horizontal so that it is caught at second base at about the same height as that catcher threw it, how much time does it take for the ball to travel the 120 feet from the catcher to second base

The time is

Explanation:

From the question we are told that

   The angle is  

    The horizontal  distance is  

Generally when the ball is at maximum height before descending the velocity is zero and this velocity can be mathematically represented as

here a =  -g  the negative sign is because the direction of motion is against gravity

So

Here is the vertical  component of the initial  velocity of the ball which is  mathematically

represented as

So      

=>    

Generally the total time taken to travel the 120 ft  is mathematically represented as

Here is the horizontal component of the initial velocity which is mathematically represented as

So

Generally the time taken to reach the maximum height is  

=>    

=>    

So

Substituting this value into the equation for total time