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. 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.

Part 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.

Part 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

Part A Answer

There are many different formulas you can use, but the simplified form that mastering physics is looking for is this one:

x₂ = d / sqrt(2kH / mg)

x₂ = d / sqrt(2kH / mg)

Part B Answer

This one seems to be what mastering physics is after:

x₂ = (x₁ * d) / (d – d₁₂)

x₂ = (x₁ * d) / (d – d₁₂)