You kick a soccer ball with a speed of 31 m/s at an angle of 50°. How long
does it take the ball to reach the top of its trajectory?

All credit goes to the person who answered this years ago:)
Reaches max height at t = 2.42s.
Explanation:
I've assumed we are neglecting air resistance. If not let me know and I'll update.
We want to examine the behaviour of the ball in the y-direction. In the absence of air resistance the only force acting on the ball is gravity, which produces an acceleration in the negative y direction. From Newton's 2nd law:
m
d
2
y
d
t
2
=
−
m
g
m
d
2
y
d
t
2
=
−
m
g
Integrating:
d
y
d
t
=
−
∫
g
d
t
d
y
d
t
=
−
g
⋅
t
+
C
From initial conditions,
d
y
d
t
=
v
y
(
t
)
,
v
0
=
v
(
0
)
=
31
⋅
sin
(
50
)
∴
v
y
(
t
)
=
v
0
−
g
⋅
t
The maximum height will be reached at
v
y
=
0
so we solve for t.
v
y
(
t
h
max
)
=
0
⇒
v
0
=
g
⋅
t
h
max
t
h
max
=
v
0
g
=
31
⋅
sin
(
50
)

An  atom  (ours, not carroll's) consists of a positively charged  nucleus, surrounded by one or more negatively charged particles called  electrons. the positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. although the nucleus is heavy, it is quite small compared with the overall size of an atom. the radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6  nm.  *  if an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.read more on -