Expert: James J. Kovalcin - 8/16/2008

Question
as an acrobat, i can safely land on the ground at speeds up to 15 meters/ second.  what is the greatest height from which i can fall?

Answer
Pretty straight forward.
If you use energy conservation, the total energy at your highest point will equal the total energy at the lowest point [the ground]. In this case the total energy at the highest point is all gravitational Ug=m*g*Dh while at the lowest point the total energy will all be kinetic Uk=1/2*m*v^2.
Just make these two equal.
m*g*Dh = 1/2*m*v^2
Solve for Dh - the change in height as you fall to the ground.
Dh = 1/2*v^2/g = 1/2*15^2/9.8 = 11.5m
By the way 15 m/sec seems a bit high to me. This corresponds to about 34 mph!