Question

Two 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.
(Image included with problem)
The target box is 2.44 m horizontally from the edge of the table. Bobby compresses the spring 1.42 cm, but the center of the marble falls 84.0 cm short of the center of the box. How far should Rhoda compress the spring to score a direct hit?
bobpursley
You want the muzzle velocity to be more by a factor of (2.44/(2.44-.84)

KE=springPE
1/2 m v^2=1/2 kx^2
so if v increases by above,
then x^2 increases by (2.44/(2.44-.84))^2

new cmpression=1.42cm*(2.44/(2.44-.84))^2

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