Can you solve the hardest physics quesiton in the world?

Question

A glass ornament of mass 575g sitting on a table is subjected to a resonant frequency of 440hz. The ornament breaks into three pieces that travel horizontally across the frictionless tabletop. Fragment A has a mass of 168g and fragment B has a mass of 212g. What is the magnitude of the momentum of the third piece of glass fragment c?

Answer 1

Yes the 440hz frequency is irrelevant and yes we can't give a numeric answer without knowing the velocity (speed and direction) of the other two fragments. But we can surely give an answer that includes these unknowns as variables.

We choose our axes so that f1 (fragment 1) is moving along the x-axis, and f2 (fragment 2) is moving at an angle 'theta' to the axis.

The magnitude of the momentum is just the length of the side that completes the triangle back to the origin, expressed in terms of p1 (magnitude of momentum of f1) and p2 (magnitude of momentum of f2) and theta.

It doesn't seem that hard at all.

Ok - law of cosines states:

c^2 = a^2 + b^2 - 2ab cos(C)

let a, b and c be the magnitude of the three momentum vectors.
if 'b' is at angle 'theta' to the x-axis, then C (the angle opposite the desired momentum vector, returning to the origin) is 180-theta.

note also cos(180 - theta) = -cos(theta)

Therefore:
c = root ( a^2 + b^2) + 2ab cos(theta)

That's it. You can express 'a' and 'b' as their momentum calculations (.168 x velocity of first fragment, .212xvelocity of second fragment) but that's the final step.

Answer 2

The 440Hz is irrelevant. Unfortunately, the velocities (both magnitude and direction) of Fragments A and B are not, and we need to know something more about them to solve the problem. If they weren't moving, we'd be okay. As it stands, we'd have to assign a velocity vector to fragment A and another to fragment B, and then give the answer in terms of VA, VB, and the various masses.

Answer 3

You cannot answer this question without knowing the vectors (direction) of each of the glass fragments.