The figure is attached below.
The initial speed of the projectile can be decomposed on to the horizontal `x` and vertical `y` axes depending on the initial firing angle.
On the horizontal (`x` axis) there in no acceleration but on the vertical axis (`y` axis) a constant acceleration will be present (the acceleration due to gravity `g` directed downwards). At maximum height the vertical speed will be zero
`V_y(hmax) =0 m/s`
If we take the positive direction on the `y` axis upwards we can write
`V_y(hmax) =V_0y -g*t`
`0 =V_0*sin(alpha) -g*t`
`t = ((V_0*sin(alpha))/g) = (60*sin(60))/9.81 =5.30 s`
Answer: the time for the projectile to reach its maximum height is 5.30 s