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?
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.