1. Given data

   • Mass of ball: $m = 0.5\,\text{kg}$
   • Initial speed: $u = 20\,\text{m s}^{-1}$
   • Final kinetic energy is $5\%$ of initial kinetic energy.

2. Initial kinetic energy $K_i = \frac{1}{2}mu^2$

3. Final kinetic energy Since the final kinetic energy is $5\%$ of the initial kinetic energy, $K_f = 0.05 K_i$

   Also, $K_f = \frac{1}{2}mv^2$

4. Relate the speeds using kinetic energy $\frac{1}{2}mv^2 = 0.05\left(\frac{1}{2}mu^2\right)$

   Cancelling $\frac{1}{2}m$ from both sides, $v^2 = 0.05u^2$

   $v = u\sqrt{0.05}$

5. Substitute $u = 20\,\text{m s}^{-1}$ $v = 20\sqrt{0.05}$

   Since, $0.05 = \frac{1}{20}$ $v = 20\sqrt{\frac{1}{20}} = \frac{20}{\sqrt{20}} = \sqrt{20} \times \sqrt{20} \times \frac{1}{\sqrt{20}}$ More directly, $v = 20 \times 0.2236 = 4.472\,\text{m s}^{-1}$

   So, $v \approx 4.47\,\text{m s}^{-1}$

6. Check options

   • A: $14.41\,\text{m s}^{-1}$ — incorrect
   • B: $19.0\,\text{m s}^{-1}$ — incorrect
   • C: $4.47\,\text{m s}^{-1}$ — correct
   • D: $1.00\,\text{m s}^{-1}$ — incorrect

Final Answer: Option C is correct.