Aplayer kicks a soccer ball from ground level and sends it flying at an angle of 30 degrees at a speed of 26 m/s. what is the maximum height attained by the ball? round to the nearest tenth of a meter.

By definition, the height is given by:
 
 Where,
 a: acceleration
 v0: initial speed
 h0: initial height.
 The initial velocity in its vertical component is:
 
 The initial height is:
  (the ball is on the ground)
 The acceleration is:
  (acceleration of gravity)
 Substituting values:
 
 Rewriting:
 
 The time in which the maximum height occurs is obtained by deriving:
  We set zero and let's time:
 
 We evaluate the time obtained in the equation of the height, to obtain the maximum height:
 
 
 The maximum height attained by the ball is:
 h (1.56) = 11.9 m

26.4 is about the right time