At time t, the ball attains a height y of
y = (30 m/s) sin(53º) t - 1/2 g t²
where g = 9.80 m/s² is the magnitude of the acceleration due to gravity.
Solve for t when y = 0:
(30 m/s) sin(53º) t - 1/2 g t² = 0
t ((30 m/s) sin(53º) - (4.90 m/s²) t ) = 0
t = 0 or (30 m/s) sin(53º) - (4.90 m/s²) t = 0
We ignore the first solution, since that refers to the moment the ball is kicked.
(30 m/s) sin(53º) - (4.90 m/s²) t = 0
(30 m/s) sin(53º) = (4.90 m/s²) t
t = (30 m/s) sin(53º) / (4.90 m/s²)
t ≈ 4.9 s
