# A Kicker punts a football from 3 feet above the ground with an initial velocity of 47 feet per second. How would an equation be written that gives the height (in feet) of the football as a function...

A Kicker punts a football from 3 feet above the ground with an initial velocity of 47 feet per second.

How would an equation be written that gives the height (in feet) of the football as a function of the time (in seconds) since it was punted?

How would I write an equation to find the height (in feet) of the football 2 seconds after the punt?  How would this be solved by showing steps?

How do I calculate  how many seconds after the punt the ball would hit the ground?

Thanks!

jerichorayel | Certified Educator

The equation that gives the height of the football as a function of the time can be expressed as:

h = -16t^2 + 47t + 3   equation1

h = height
t = time

To find the height of the football 2 seconds after the punt:

t = 2
h = -16t^2 + 47t + 3

h = -16(2)^2 + 47(2) + 3
h = -64 + 94 + 3
h = 33 ft.
The height of the football 2 seconds after the punt is 33ft.

To find the time (seconds) the football would hit the ground, equate the equation 1 to 0 (h =0) then solve for t.

-16t^2 + 47t + 3 = 0
(-16t^2 + 47t + 3 = 0)x-1
16t^2 -47t -3 = 0
(16t +1)(t-3) = 0

t = -1/16 and t = 3

We can ignore the negative root (-1/6).

t = 3 seconds
The football strikes the ground 3 seconds after it is punted.