Problems for Intermediate Methods in Theoretical Physics Edward F. Redish

Consider the simple case of a ball thrown straight up starting at a position y = 0 with an initial upward velocity of magnitude v_y(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, v_y(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, t_m, at which the ball reaches its maximum height.

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

RETURNS

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Last revision 16. October, 2005.