Final answer:
The hang time of a football kicked at an initial speed of 27.5 m/s and a launch angle of 56.7 degrees is calculated by finding the vertical component of the initial velocity, doubling it, and then dividing it by the acceleration due to gravity.
Step-by-step explanation:
To calculate the hang time or the total time a football is in the air after being kicked, we can use kinematic equations for projectile motion. The hang time is determined by the vertical component of the initial velocity and the acceleration due to gravity. Given that the initial speed of the football is 27.5 m/s and the launch angle is 56.7 degrees, we can calculate the vertical component (Vy) of the initial velocity using the sine function: Vy = 27.5 m/s * sin(56.7 degrees).
The formula for the hang time (T) in projectile motion, when the object lands at the same vertical level from which it was launched is T = 2 * Vy / g, where 'g' is the acceleration due to gravity (9.81 m/s^2). Plugging in the computed value of Vy into this formula will give the hang time.
Remember, this calculation assumes no air resistance and a level field where the ball is kicked and lands at the same height. Thus, the hang time is just the time it takes for the ball, under the influence of gravity alone, to rise to its highest point and then fall back to the launch level.