Afootball player punts the ball from the ground at a 65.0° angle above the horizontal. if the ball stays in the air for a total of 6.5 seconds, what are the vertical and horizontal components of the initial velocity?

Explanation:

Hi!

We define the point (0,0) as the intial position of the ball. The initial velocity is

The motion of the ball in the horizontal direction (x) has constant velocity, because there is no force in that direction. :

In the vertical direction (y), there is the downward acceleration g of gravity:

(note the minus sign of acceleration, because it points in the negative y-direction)

When the ball hits the ground, at t = 65s,  y(t = 65 s) = 0. We use this to find the value of the initial vertical velocity:

We used that g = 9.8 m/s²

To find the horizonttal component we use the angle:

snell's law

refractve index = sin incidence / sin refraction