Answer to Question #95431 in Physics for louis

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.The target box is horizontal distance

Answer 1

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 = 2.20 m from the edge of the table. Bobby compresses the spring 1.10 cm, but the center of the marble falls 27.0 cm short of the center of the box. How far should Rhonda compress the spring to score a direct hit? 

For Bobby

$$t=\frac{D-d}{v}$$

From the conservation of energy:

$$0.5mv^2=0.5kx^2$$

$$\frac{k}{m}=\frac{v^2}{x^2}$$

For Rhonda

$$t=\frac{D}{V}$$

$$0.5mV^2=0.5kx'^2$$

$$V=v\frac{D}{D-d}$$

Thus,

$$\left(v\frac{D}{D-d}\right)^2=\frac{v^2}{x^2}x'^2$$

$$x'=x\frac{D}{D-d}=1.1\frac{2.2}{2.2-0.27}=1.25\ cm$$