Given data
The duration of the ball traveled is t = 3 s
The expression for the vertical distance is given as:
![S=(1)/(2)gt^2](https://img.qammunity.org/2023/formulas/physics/college/9rtjnvn4akgo260vmbxd67x6e19znktaia.png)
The acceleration due to gravity is taken as g.
Substitute the value in the above equation.
![\begin{gathered} S=(1)/(2)*10m/s^2*(3s)^2 \\ S=45\text{ m} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/9pi2832z0x6xhew2q8tvr5ce574qwitlxa.png)
Thus, the vertical distance is 45 m.
Thus, the correct option is (c).