Question

Soccer player kicks a ball down field. The ball's initial velocity is 30 m/s, 30 degrees above horizontal.

a) What is the ball's horizontal velocity at the maximum height of the ball's trajectory?

b) What is the horizontal displacement of the ball just before it lands down field?

Answer 1

There is no horizontal force on the ball.
So why would its horizontal velocity change?
It does not, until it hits the ground or is headed or kicked.
u =30 cos 30

Q : How long is it in the air?
A : Twice as long as it takes to stop moving up at the top of its trajectory

Q : How long does it take to get to the top?
A : v = Vi - g t
v = 0 at the top
but Vi = 30 sin 30 = 15 m/s
so 0 = 15 - g t
so
t = (15/9.8) seconds to the top
so time in air = 2 t = 30/9.8

Q : How far does it go down the field in (30/9.8) seconds?
A : (30/9.8) u = (30/9.8)(30 cos 30)