Question

Ray Guy is a punter who was elected to the NFL Hall of Fame. One of his punts was kicked at 74° above the ground with a 6.2 second hang time. Determine the speed (m/s) with which the ball was punted. (Assume the acceleration due to gravity is 9.81 m/s/s) *

Answer 1

The speed with which Ray Guy punted the ball is approximately 40.56 m/s.

Step-by-step explanation:

Ray Guy's punt can be analyzed using the kinematic equation for projectile motion. The vertical motion of the ball can be described by the equation
`h = ut + (1/2)gt^2`, where h is the height, u is the initial vertical velocity, g is the acceleration due to gravity, and t is the time of flight. In this case, the ball is kicked at an angle of 74°, so the initial vertical velocity (u) can be found using the equation u = usinθ, where θ is the launch angle. Substituting the given values, we get u = 40.056 m/s.

Next, we can use the hang time to find the total time of flight (T) using the equation T = 2usinθ / g. Substituting the known values, we find T = 6.2 seconds. Now, we can use the horizontal motion equation, d = ut + (1/2)at^2, to find the horizontal distance traveled by the ball. Since there is no horizontal acceleration, this simplifies to d = ut, and we can find the horizontal velocity (v) using the equation v = d / T. Substituting the values, we get v = 32.5 m/s.

Finally, to find the overall speed (V) of the punt, we use the Pythagorean theorem:
`V = sqrt(u^2 + v^2)`. Substituting the calculated values, we find V ≈ 40.56 m/s. Therefore, the speed with which Ray Guy punted the ball is approximately 40.56 m/s, showcasing the impressive athleticism and skill required for such precise kicks.