A toy gun consists of a spring and a  rubber dart of mass 16g. When compressed by 4cm and released, it projects the dart to a height of 2m. If compressed by 6cm, the height achieved is

If k is the spring factor, then P.E of the spring compressed by distance x(=12kx2)  will equal to gain in P.E. of the dart (=mgh)  i.e. 12kx2=mgh ∴12k(4)2=16×g×200...................(i)And 12k(6)2=16×g×h...................(ii)On solving , (i) and (ii), we get h = 450cm = 4.5m.h+xα x2   ∵ mgh+x=k x22