Question

An NFL punt covered 41.1 meters and the hang time was 4.44 seconds. At what angle was the football punted?

Answer 1

The range is

$$R=\frac{v^2}{g}\sin{2\theta}$$

Time of flight:

$$T=\frac{2v}{g}\sin{\theta}\to v=\frac{gT}{2\sin{\theta}}$$

$$R=\frac{(\frac{gT}{2\sin{\theta}})^2}{g}\sin{2\theta}$$

$$R=\frac{gT^2}{4}\cot{\theta}$$

$$41.1=\frac{(9.8)(4.44)^2}{4}\cot{\theta}$$

$$\cot{\theta}=0.85096$$

$$\theta =\arcctg{0.85096}=49.6\degree$$