$$v_i = \sqrt{\frac{2gh}{\sin^2\theta}}$$
where:
* \(v_i\) is the initial velocity in meters per second (m/s)
* \(g\) is the acceleration due to gravity (9.8 m/s²)
* \(h\) is the maximum height reached by the football in meters (m)
* \(\theta\) is the angle at which the football is kicked in degrees
In this case, we have:
* \(h = 4.7\) m
* \(\theta = 20\degree\)
Plugging these values into the equation, we get:
$$v_i = \sqrt{\frac{2(9.8 \text{ m/s}^2)(4.7 \text{ m})}{\sin^2(20\degree)}}$$
$$v_i = 15.6 \text{ m/s}$$
Therefore, the initial velocity of the football is 15.6 m/s.
