We use the equation of motion,
\(v=u+at\).
Here, v is final velocity, u is initial velocity and a = - g (acceleration due to gravity) because ball thrown vertically into air.
At maximum height, the final velocity becomes zero, i.e v = 0.
Thus equation becomes,
\(0=u-gt\\\\t=\frac{u}{g}\).
Given, \(u=130\ ft/s\) and we take \(g=9.8\ m/s^2=9.8\times3.2 \frac{ft}{s^2} =32.14\ ft/s^2\).
Substituting these values in above equation, we get
\(t=\frac{130\ ft/s}{32.14\ ft/s^2} =4.05\ s\).
Thus, to reach the maximum height the time taken by the ball is 4.05 s.
