Final answer:
Using the given initial speed and launch angle, the equation of projectile motion was applied to determine the horizontal range of the football. The calculation shows that the football travels approximately 3.93 s^2 before hitting the ground, which does not match the provided answer choices, indicating a possible error in the question or options.
Step-by-step explanation:
To determine how far the football travelled before hitting the ground, we can use the equations of motion for projectile motion. The initial speed of the football is given as v0 = 20 m/s and the launch angle is θ = 37.0°. The horizontal distance (range) R can be calculated using the range formula for projectile motion:
R = ϕ(v0)2sin(2θ) / g
where g = 9.81 m/s2 is the acceleration due to gravity. First, we convert the launch angle to radians for calculation:
θ (in radians) = θ (in degrees) × (pi / 180)
θ (in radians) = 37.0 × (π / 180) ≈ 0.6458 radians
Then we substitute the values into the range formula:
R = ϕ(20 m/s)2sin(2 × 0.6458) / 9.81 m/s2
R ≈ 40.0 m (sin(1.2916)) / 9.81 m/s2
R ≈ 40.0 m (0.9636) / 9.81 m/s2
R ≈ 38.544 m / 9.81 m/s2
R ≈ 3.93 s2
Therefore, the football travels approximately 3.93 s2 before hitting the ground. The provided options A to D do not match this result, hence there may be an error in the question prompt or the options provided.