A football is punted up into the air and it lands 5 seconds later. How high did the did the football reach it's highest point and when does it reach this height?

t(up) = t(dn) = 5/2 = 2.5s.

Vf = Vo + gt,
Vo = Vf - gt,
Vo = 0 - (-9.8)*2.5 = 24.5m/s.

h = (Vf^2 - Vo^2) / 2g,
h = (0 - (24.5)^2 / -19.6 = 30.6m.

To find the height the football reached at its highest point, we need to use a few principles of physics.

First, we need to understand that when an object is in free fall, the time it takes to reach its highest point is the same as the time it takes to fall back down to its starting point. So, in this case, the football took 5 seconds to reach its highest point.

Secondly, we can use the concept of projectile motion. When an object is launched into the air, it follows a parabolic path. The height it reaches depends on the initial velocity, the angle of projection, and the acceleration due to gravity.

However, since we are given only the time it took for the football to reach its highest point, we'll assume that the initial velocity and angle of projection remain constant. Let's call the time it takes for the football to reach its highest point "t".

So, using the principles of physics, we can derive the following equation:

h = V₀ * t - (1/2) * g * t²

Where:
h = height reached
V₀ = initial velocity of the football
t = time taken to reach highest point
g = acceleration due to gravity (approximately 9.8 m/s²)

Since we're given that it took 5 seconds to reach the highest point, we can substitute this value into the equation:

h = V₀ * 5 - (1/2) * 9.8 * (5)²

Simplifying further:

h = 5V₀ - (1/2) * 9.8 * 25
h = 5V₀ - 122.5

Now, we need the initial velocity of the football to find the value of "h". Unfortunately, the initial velocity is not provided in the question. If you have any additional information, please provide it so that we can proceed with finding the highest point.