What would be the time of flight, maxiumum height and horizontal range of the football was kicked from the floor? if a field goal attempt was made from 40 yards (36.58 m) and the goal post is 10 feet tall (3.084 m) will the kicker make the field goal?

Answers:

a) 3.511 s

b) 15.1062 m

c) 86.281 m

Explanation:

Assuming the initial velocity of the ball is and the angle  , we have the following data:

the distance between the football player and the the goal post

the height of the goal post

Now, this can be solved with the following equations related to parabolic motion:

(1)

(2)

(3)

Where:

is the time of flight

is the acceleration due gravity

is the maximum height, when the time is half the time of flight

is the initial height

is the horizontal range

Knowing this, let's begin with the answers:

We will use equation (1):

(4)

(5)

In this case, we have to use equation (2) and substitute the calculated  in (5):

(6)

(7)

Let's use equation (3):

(8)

(9)

Since the maximum height and the horizontal range of the ball are greater than and , we can say the kicker is able to make the field goal.

this could be newton#'s law of cooling. the cooling curve is exponential