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need a little help with my physics?
2 children are playing a game in which they try to hit a small box on the floor with a marble fired from a spring-loaded gun that is mounted on a table. The target box is horixontal distance D=2.2m from the edge of the table. The boy compresses the spring 1.1cm but the center of the marble falls 27cm short of the senter of the box. how far should he compress the spring to score a direct hit? (this problem has no friction)
any help would be appreciated.
thanks.
by conservation of energy 1/2 K x^2 = m g S, where S is the stopping distacne of marble.
hence, x is prportional to square root of S and x1 / x2 = square root of ( S1/S2)
or, 1.1 / x2 = square root of ( 1.93 / 2.2 )
and compression of the spriong x2 = 1.1 x sauare root of (2.2 / 1.97 )
= 1.1624 cm.
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