Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Natural scales in flat-earth gravity

Consider the simple case of a ball thrown straight up starting at a position y = 0 with an initial upward velocity of magnitude vy(t=0) = v0. Treat gravity in the flat-earth approximation and ignore air resistance.

(a) Using dimensional analysis, create a “natural length” from the parameters of this problem. (What are appropriate constants to use for this task?)

(b) Find the position, y(t), and velocity, vy(t), of the ball as a function of time. (Hint: One good way to do this is to start from the equation of motion, N2, and integrate.)

(c) Find the time, tm, at which the ball reaches its maximum height.

(d) Make a Taylor series for the height of the ball, y(t), about tm. Keep terms through the second order.

This page prepared by

Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120

Last revision 28. Decmber, 2010.