In order to find if the projectile reaches 100 ft of height, let's use h(t) = 100 in the equation and solve it for t:

Using the quadratic formula to solve this equation, we have:
![\begin{gathered} a=1,b=-5,c=6 \\ t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t_1=\frac{5+\sqrt[]{25-24}}{2}=(5+1)/(2)=3 \\ t_2=(5-1)/(2)=2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/4uq46o3w1o8u154efwcvnngrv6a8bfemj1.png)
Since we have two valid results of t, the answer is yes, the projectile first reaches 100 meters at t = 2 seconds (when the projectile is going upwards) and then it reaches again when it's going down (at t = 3 seconds).