Explanation

(b) Given ,m=2kg,v=3$ms^{- 1},K = 144Nm^{- 1}$
Let spring is compressed by a length x.
$ie\frac{1}{2}mv^{2} = \frac{1}{2}kx^{2}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \frac{1}{2} \times 2 \times (3)^{2} = \frac{1}{2} \times 144 \times x^{2}$
Or $\ \ \ \ \ \ \ \ \ 9 = 72x^{2}$
Or $\ \ \ \ \ \ \ \ \ \ x = \sqrt{\frac{9}{72}} = \frac{1}{2\sqrt{2}}m$
Hence, length of compressed spring
$= 2 - \frac{1}{2\sqrt{2}}$
$= \frac{4\sqrt{2} - 1}{2\sqrt{2}} = 1.5m$