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The impact crater of a small metal ball of 63.7 grams (0.0637kg) is dropped from 8 different heights, ranging from 0.20m to 0.90m was observed. A mean was measured for the craters diameter. Using the equation E=mg$\Delta$h given that we have m, and g is a constant of 9.81 we can find the kinetic energy of the ball on impact. The relationship between crater diameter, D, and impact energy, E, is given by D=kE$^n$ where K is constant and n is found by the gradient of the graph and is also constant. This can be modified to give $\log D = n\log E + \log k$.

Template for C240 Models of Computation Assessed Coursework 2
Contains macros for typesetting register machines in textual, graphical and encoded formats.
Department of Computing, Imperial College London
This work is released into the Public Domain.

phase1-AR.tex (use only for Archival Research and Theory proposals; use phase1-GO.tex
for General Observer and Snapshot proposals and phase1-DD.tex for GO/DD
proposals or use phase1-MC.tex for GO/MC rapid response proposals.
HUBBLE SPACE TELESCOPE
PHASE I ARCHIVAL & THEORETICAL RESEARCH PROPOSAL TEMPLATE
FOR CYCLE 25 (2017)
Version 1.0, January 2017
Guidelines and assistance
Cycle 25 Announcement Web Page
Please contact the STScI Help Desk if you need assistance with any
aspect of proposing for and using HST. Either send e-mail to
help@stsci.edu, or call 1-800-544-8125; from outside the United
States, call [1] 410-338-1082.

This problem is an applied optimization problem. The problem is to minimize
the area of the triangle formed by a tangent line to the function y = 1⁄9 x2.
The triangle is defined by the origin, the x-intercept of the tangent line, and the
y-intercept of the tangent line. Only triangles formed in the first quadrant are
of concern.