Given data
*The given distance from the base of the ledge is R = 2.25 m
*The given speed is v = 3.5 m/s
The diagram is given below
(a)
Let (h) be the height of the edge
The formula for the distance from the base of the ledge is given as
![\begin{gathered} R=v* t \\ R=v*\sqrt[]{(2h)/(g)} \\ h=(R^2* g)/(2v^2) \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/43e6gqli956r8gaff0prgtgqnwik0pcepw.png)
Substitute the known values in the above expression as

Hence, the height of the ledge is h = 2.025 m
(b)
The formula for the time taken by the boulder to fall to the bottom of the cliff is given as
![t=\sqrt[]{(2h)/(g)}](https://img.qammunity.org/2023/formulas/physics/college/bf4ls0n97d0h2dgi9qjnvaysom2eznam6b.png)
Substitute the known values in the above expression as
![\begin{gathered} t=\sqrt[]{(2*2.025)/(9.8)} \\ =0.642\text{ s} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/8t52kbgus6t7lzbbf3mwnri8i2ngwfahtn.png)
Hence, the time taken by the boulder to fall to the bottom of the cliff is t = 0.642 s