We are only interested in the vertical motion of the ball, in order to solve the problem.
The vertical motion of the ball is an uniformly accelerated motion, with constant acceleration [tex]a=g=-9.81 m/s^2[/tex] (acceleration of gravity). Therefore, the vertical velocity at time t is given by
[tex]v_y (t) = v_{y0} +at[/tex]
where [tex]v_{y0}=7.5 m/s[/tex] is the initial vertical velocity of the ball.
The ball reaches its highest point when [tex]v_y(t)=0[/tex]: therefore, substituting this information into the equation, we can calculate the time t at which this happens:
[tex]0=v_{y0}+at[/tex]
[tex]t=-\frac{v_{0y}}{a}=-\frac{7.5 m/s}{9.81 m/s^2}=0.765 s[/tex]
