Since the ball is moving by uniformly accelerated motion, its vertical velocity at time t is given by
[tex]v(t)= v_0 - a t [/tex]
where we took upward as positive direction, and where [tex]v_0[/tex] is the initial velocity, a the acceleration and t the time.
The instant at which [tex]v(t)=0[/tex] is the instant when the ball reverses its velocity (from upward to downward). This means that the difference between the time t at which v(t)=0 and the instant t=0 is the total time during which the ball was going upward:
[tex]0=v_0 - at[/tex]
By plugging numbers into the equation, we find
[tex]t= \frac{v_0}{a}= \frac{56 ft/s}{32 ft/s^2}=1.75 s [/tex]
