# Question

A huge boulder is inadvertently cast high into the air during an open pit mine blast. Using the definition of mass center and Newton’s second law of motion, show that the center of mass of the boulder travels the same path even if it disintegrates into 1,001 pieces of various sizes and shapes.

## Answer to relevant Questions

Suppose a static factor of safety is defined as the ratio of resisting to driving forces, that is, FS = R/D. Show that a factor of safety less than one implies acceleration is impendingLet f : R2 →R be defined by f(x, y) = { x|y| / √x2 + y2 (x, y) ≠ 0, 0 (x, y) =0.A function f: Rn x Rm→ Rp is bilinear if for x,x1, x2 € R n, y,y1, y2 € Rm and a € R\ We have, f(ax, y) = af (x, y) = f(x, ay) f(x1 + x2, y) = f(x1, y) + f(x2, y) f(x, y1 +y2) = f(x, y1) + f(x, y2) ...Define f: R → R by f (x) = { e-x-2 x ≠ 0,. 0 x -0,} a. Show that f is a C00 function, and f(i) (0) = 0for all .Let f: R2 → R be defined as in Problem 1-26. Show that Dxf (0, 0) exists for all x, although f is not even continuous at (0,0).Post your question

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