Distance between the goal posts, 19.5 feet, is the length of an arc on a circle of radius 50 yards. The kicker aims to kick the ball midway between the uprights. To score a field goal, what is the maximum number of degrees that the actual trajectory can deviate from the intended trajectory? What is the maximum number of degrees for a 20-yard field goal?

Question

So I know that the length is 19.5 feet, and since 3 feet = 1 yard, that the 50 yard radius = 150 feet radius of circle.

I'm stuck in what to do next? Please help.

Answer 1

let's stick with yards. The distance between the goal posts is 6.5 yards.

So, since arc length s = rθ, we want θ such that

50θ = 6.5
θ = 0.13 radians = 7.45°

But, he can only deviate by 1/2 that, or 3.72°

Plug in r=20 for the other part.

Technically, the distance between the posts is the chord of the arc, but this is what the problem stated, and it is easier to deal with.