Two children are playing a game in whichthey try to hit a small box on the floor

Question

   Two children are playing a game in whichthey try to hit a small box on the floor with a marble fired from aspring loaded gun that is mounted on a table. The target box ishorizontal distance D=2.20m from the edge of the table. Bobbycompressed the spring 1.10cm, but the center of the marble falls27.0cm short of the center of the box. How far should Rhodacompress the spring to score a direct hit? Assume that neither thespring nor the ball encounters friction in the gun. Please explainand include units.

Explanation / Answer

Two children are playing a game in which they try tohit a small box on the floor with a marble fired from a springloaded gun that is mounted on a table. The target box is horizontaldistance D=2.20m from the edge of the table. Bobby compressed thespring 1.10cm, but the center of the marble falls 27.0cm short ofthe center of the box. How far should Rhoda compress the spring toscore a direct hit? Assume that neither the spring nor the ballencounters friction in the gun. Please explain and includeunits.
the distance to be reached depends upon how the spring iscompressed.
so
1/2*k*1.1*1.1=F*(220-27)=F(193)
hence
1/2K*1.1*1.1 193 ---1
    1/2K*x*x 220 ---2
solving we get x=1.1744cm
so Rhoda should compress the spring to 1.1744cm toscore a direct hit.ng nor

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