On ihe Vis viva. 285 
MECHANICAL PROBLEMS; 
The solutions of which depend for the most 
pari on the preceding theorems. 
Prosiem I. Ifa cube, whose height = 
inch, and weight =1 pound, move with the 
velocity acquired by falling freely through 
193 inches, and strike with one of its faces 
an indefinite mass of soft matter, which it 
penetrates to the depth of 7-72 inches before 
its velocity is destroyed: required a weight 
which is equal to the resistance of the matter 
to the face of the cube ? 
Sotutrion. We have in cor. 4, theor. 2. 
a=1=6b; S193; s=7: = 3 hence p or 
the required weight, equal 4S. 5 __ 95 itys) 
s 
$ 
Q.E.L. 
Progiem If. Ifa sphere, and cube equal 
to its circumscribing cube, move with equal 
velocities, and fall upon an indefinite bed of 
matter, having an uniform resistance, in such 
a manner that the cube strikes the bed with 
one of its faces, and sinks m inches perpendi- 
cularly into it: what is the perpendicular 
depth to which the sphere will sink; supposing 
the bodies to be homogeneous, and neglecting 
the action of gravity ? 
