A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20ms⁻¹. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now?

by conservation of mechanical energy

              K.E_i + P.E_i = K.E_f + P.E_f

              $\frac{1}{2}\times 0.5v^2+0=\frac{1}{2}\times 0.5{\left(\frac{v}{2}\right)}^2+\frac{1}{2}k{x}^2$  

              $\Rightarrow \frac{1}{2}\times 0.5\left[v^2-\frac{v^2}{4}\right]=\frac{1}{2}k{x}^2$  

              $\Rightarrow \frac{1.5}{4}12\times 12=\frac{k\times 9}{100}$  

              $\frac{1.5\times 36}{9}\times 100=k$  

              k = 600 N/m¹