Question

Two children are trying to shoot a marble of mass m into a small box using a spring-loaded gun that is fixed on a table and shoots horizontally from the edge of the table. (Figure 1)The edge of the table is a height H above the top of the box (the height of which is negligibly small), and the center of the box is a distance d from the edge of the table. The spring has a spring constant k. The first child compresses the spring a distance x1 and finds that the marble falls short of its target by a horizontal distance d12.

A)

By what distance, x2, should the second child compress the spring so that the marble lands in the middle of the box? (Assume that height of the box is negligible, so that there is no chance that the marble will hit the side of the box before it lands in the bottom.)

Express the distance in terms of m, k, g, H, and d.

B)

Now imagine that the second child does not know the mass of the marble, the height of the table above the floor, or the spring constant. Find an expression for x2 that depends only on x1 and distance measurements.

Express x2 in terms of x1, d, and d12.

Answer 1