Afootball player kicks a ball with an initial upward velocity of 47 ft./s. the initial height of the ball is 3 feet. the function h(t)=-16t^2+vt+h0 models the height (in feet) of the ball, where v is the initial upward velocity and h0 is the initial height. if no one catches the ball, how long will it be in the air?

3 seconds

We are given the following function:

   (1)

Where:

is the time the ball is in the air

the initial upward velocity

the initial height of the ball

is the final height of the ball. If no one catches it, this will be zero

So, equation (1) changes to:

   (2)

Substituting the known values:

   (3)

This is a quadratic equation in the form . In order to find we can use the quadratic formula for the roots:

   (4)

Where , and  

Substituting this values in (4):

   (5)

   (6)

   (7)

For :

     (8)>>>> This result does not work for us because is negative

For :

  (9)>>>This is the result

Therefore:

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8