Final answer:
To find the maximum height of the football punted at an angle, we use the formula involving the vertical component of the initial velocity and the acceleration due to gravity. The correct maximum height of the football is calculated to be 5.10 meters, which is not listed in the question options.
Step-by-step explanation:
To calculate the maximum height (H) of a football punted at an angle with an initial velocity, we need to use the vertical component of the initial velocity and the acceleration due to gravity. The formula to calculate the maximum height is given by:
H = (v_0^2 × sin(² heta)) / (2 × g)
Where v_0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (approximately 9.81 m/s²). We're given:
- Initial velocity, v_0 = 20.0 m/s
- Launch angle, θ = 30°
- Acceleration due to gravity, g = 9.81 m/s²
First, we find the vertical component of the initial velocity:
v_0y = v_0 × sin(θ) = 20.0 m/s × sin(30°) = 10.0 m/s
Next, we use the formula to find the maximum height H:
H = (v_0y^2) / (2 × g) = (10.0 m/s)^2 / (2 × 9.81 m/s²) = 5.10 m
So, the maximum height of the football vertically is not listed in the options provided in the question, so there seems to be an error with the options given. However, using the correct method, the maximum height is indeed found to be 5.10 m.