A punted football is observed to have velocity components vhorizontal = 15 m/s to the right and vvertical = 1.25 m/s directed downward at a height h = 1.3 m above the ground. Use a Cartesian coordinate system with the origin located on the ground at the position the football was punted and assume it encountered no air resistance. Determine the football's initial horizontal velocity magnitude v h in terms ofw roe in. Wermeal, g, and h.

This is a projectile launch problem. The horizontal speed that is constant throughout the entire path is worth 15 m / s, instead the vertical speed changes in value due to the acceleration of gravity, let's look for the initial vertical speed

Vy² =[tex]v_{oy}[/tex]² - 2 g y

[tex]v_{oy}[/tex]² = [tex]v_{y}[/tex]² + 2 g y

[tex]v_{oy}[/tex] = √ ([tex]v_{y}[/tex]² + 2 gy

Let's calculate

[tex]v_{oy}[/tex] = √ (1.25² + 2 9.8 1.3)

[tex]v_{oy}[/tex] = √ (27.04)

[tex]v_{oy}[/tex] = 5.2 m / s

The initial speed can be calculated by the initial speed

v = √ v₀ₓ² + [tex]v_{oy}[/tex]²

v = RA (15² + 5.2²)

v = 15.87 m / s

We look for the angle with trigonometry

tan θ = voy / vox

θ = tan⁻¹ I'm going / vox

θ = tan⁻¹ 5.2 / 15

θ = 19.1

The answer is

v₀ₓ = 15 m / s

[tex]v_{oy}[/tex] = 5.2 m / s