In the figure here, two children are playing a game in which they try to hit a s

Question

In the figure here, 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. The target box is horizontal distance D = 2.16 m from the edge of the table. Bobby compresses the spring 1.11 cm, but the center of the marble falls 25.1 cm short of the center of the box. How far should Rhoda compress the spring to score a direct hit? Assume that neither the spring nor the ball encounters friction in the gun.

Explanation / Answer

conservation of energy

1/2*k*x^2 = 1/2*m*v^2

velocity is directly proportional to velocity

time taken = T = sqrt(2H/g )

in time T ball travels VoT distance

velocity is proportional to distance

spring compression is also proportional to distance

X(rhoda) / X(bobby) = 2.16 / ( 2.16 - 0.251)

X(rhoda) / 1.11cm = 2.16m/ 1.909m

X(rhoda) = 1.11 * 2.16 / 1.909

X(rhoda) = 1.2559 cm

he should compress 1.26 cm

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