Question

A professional football team uses computers to describe the projectile motion of a football when punted. After compiling data from several games, the computer models the height of an average punt with the equation h(t) = ((-16)/3)(t - 2.2)^2 + 26.9 where t is the time in seconds and h(t) is the height in yards. The punter’s foot makes contact with the ball when t = 0. Find h(3) and explain the meaning of this value.

Answer 1

To determine the height of the football at 3 seconds after being punted, we calculate h(3) by substituting 3 into the provided quadratic equation. The resulting height is approximately 23.1 yards, indicating how high the football is above the ground at that time.

Step-by-step explanation:

To find h(3) which represents the height of the football at 3 seconds after being punted, we plug the value of t into the given equation: h(t) = ((-16)/3)(t - 2.2)^2 + 26.9. Calculating this, we get h(3) = ((-16)/3)(3 - 2.2)^2 + 26.9. Performing the operations, h(3) equates to

h(3) = ((-16)/3)(0.8)^2 + 26.9

h(3) = ((-16)/3)(0.64) + 26.9

h(3) = (-16/3)(0.64) + 26.9

h(3) = -10.24/3 + 26.9

h(3) equals approximately 23.1 yards.

The meaning of this value is that, at 3 seconds after being punted, the football is approximately 23.1 yards above the ground.