Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Time of flight

A spring-loaded cannon launches a tennis ball upward at an angle θ0 with a speed v0. Assume that it is launching it from the ground and the ground is level and horizontal.

(a) Write Newton's second law as a vector differential equation for the vector velocity assuming that you can get away with assuming a purely viscous drag. (Not a good assumption!)

(b) Separate your vector equation into two ordinary differential equations for the x and y components of the velocity.

(c) Using your dimensionless form from last week, simplify and find a general solution for these equations.

(d) Show that the time that the ball is in the air satisfies the (dimensioned) equation

This page prepared by

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

Last revision 19. September, 2004.