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


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

Last revision 19. September, 2004.