physic question
posted by mujisen .
Two children are playing a game in which they try to hit a small box on the floor with a marble fired from a springloaded gun that is mounted on a table. The target box is horizontal distance D = 2.15 m from the edge of the table, see the figure. Bobby compresses the spring 1.10 cm, but the center of the marble falls 23.0 cm short of the center of the box. How far should Rhoda compress the spring to score a direct hit?

kx²/2=mv²/2
v=x•sqrt(k/m)
t=sqrt(2h/g)
s=v•t= x•sqrt(k/m) • sqrt(2h/g) =>
s1= x1•sqrt(k/m) • sqrt(2h/g)
s2= x2•sqrt(k/m) • sqrt(2h/g)
s1/s2=x1/x2
x2=x1•s2/s1 =1.1 (2.15/(2.150.23) =1.23 cm