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 larger box is horizontal distance D = 2.19 m from the edge of the table. Bobby compress the spring 1.24 cm, but the center of the mantle falls 25.7 cm short of the center of the box. How far should shads compress the spring to score a direct hit? Assume that neither the spring nor the ball encounters friction in the gun.

Explanation / Answer

Applying energy conservation to find speed of ball just after it leaves spring.

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

v = sqrt(k/m) x

ball leave table horizontally,

and height of table does not change so time it take to reach the ground will be same.

say it is t.

then D = v t

D = sqrt(k/m)tx

term sqrt(k/m) t is constant so D is propotional to the x.

d1 / d2 = x1 / x2

2.19 / (2.19 - 0.267) = x / 1.24

x = 1.41 cm

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