Given, \(​ h = 15 ~\text m~~,v = 1 ~\text{m/s},~~m= 10~\text{kg}, ~~g = 10 ~\text{m/s}^2 ​\)

Step 1: Find the final kinetic energy.
From the conservation of mechanical energy.
\(\left(\right. PE \left.\right)_ i + \left(\right. KE \left.\right)_ i = \left(\right. PE \left.\right)_ f + \left(\right. KE \left.\right)_ f \)
\(\Rightarrow   mgh + \frac{1}{2} \left(mv\right)^{2} = 0 + \left(\right. KE \left.\right)_ f \)
\( \Rightarrow   \left(\right. KE \left.\right) f = mgh + \frac{1}{2} \left(mv^{2}\right)\)
\(\Rightarrow   \left(\right. KE \left.\right) _f = 10 \times 10 \times 1 .5 + \frac{1}{2} \times 10 \times \left( 1^{2} \right)\)
\(\Rightarrow 150 + 5 = 155 ~\text J\)

Hence, option (4) is the correct answer.$\begin{array}{l}\mathrm{}\end{array}$