Write a program to provide information on the height of a ball thrown straight up into the air. The program should request as input the initial height, h feet, and the initial velocity, v feet per second. The height of the ball after t seconds is

The height of the ball after t seconds is h + vt - 16t 2 feet:

def main():

getInput()

def getInput():

h = int(input("Enter the initial height of the ball: ")) # Adding the int keyword before input() function

v = int(input("Enter the initial velocity of the ball: ")) # Same as above

isValid(h,v)

def isValid(h,v):

if ((h <= 0) or (v <= 0)):

print("Please enter positive values")

getInput()

else:

maxHeight(h,v)

def maxHeight(h,v):

t = (v/32)

maxH = (h + (v*h) - (16*t*t))

print ("\nMax Height of the Ball is: " + str(maxH) + " feet")

ballTime(h, v)

def ballTime(h,v):

t = 0

ballHeight = (h + (v*t) - (16*t*t))

while (ballHeight >= 0):

t += 0.1

ballHeight = (h + (v*t) - (16*t*t))

print ("\nThe ball will hit the ground approximately after " + str(t) + " seconds")

# Driver Code

main()

I am writing a python code.

def getInput():

   h = int(input("enter the height: "))

   v = int(input("enter the velocity: "))

   isValid(h,v)    

def isValid(h,v):

   if (h<= 0 or v<=0):

       print("not positive ")            

   else:

       height = maximumHeight(h,v)

       print("maximum height of the ball is", height," ft.")

       balltime = ground_time(h,v)

       print("The ball will hit the ground after", balltime, "s approximately.")

def maximumHeight(h,v):

   t = (v/32)

   maxheight = (h + (v*t) - (16*t*t))

   return maxheight    

def ground_time(h,v):

   t = 0.1

   while(True):

       heightofball = (h + (v*t) - (16*t*t))

       if (heightofball <= 0):

           break

       else:

           t += 0.1  

   return t

Explanation:

There are four functions in this program.

getInput() function is used to take input from the user which is height and velocity. h holds  the value of height and v holds the value of velocity. input() function is used to accept values from the user.

isValid() function is called after the user enters the value of height and velocity. This function first checks if the value of height and velocity is less than 0. If it is true the message not positive is displayed. If its false then maximumHeight() is called which returns the maximum height of the ball and function ground_time() is called to return the time when the ball will hit the ground.

maximumHeight() function first divides the value of velocity with 32 as the ball will reach its maximum  height after v/32 seconds. It then returns the maximum height by using the formula:  heightofball = (h + (v*t) - (16*t*t)).

ground_time() calculates the time the ball takes to reach the ground. There is a while loop to height after every 0.1 second and determine when the height is no longer a positive . It uses (h + (v*t) - (16*t*t)) formula to calculate the height and when the value of height gets less than or equal to 0 the loop terminates otherwise it keeps calculating the height while adding 1 to the value of t at each iteration. After the loop breaks, it returns the value of t.

To see the output of the maximum height and time taken by ball to reach the ground, you can call the getInput() function at the end of the above program as:

getInput()

Output:

enter the height: 9

enter the velocity: 10

maximum height of the ball is 10.6525  ft.

the ball will hit the ground after 1.2 s approximately.

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