The Doppler Effect Suppose a rocket is fired upward from the surface of the earth with a initial velocity v (measured in meters per second). Then the maximum height h (in meters) reached by the rocket is given by the function Ru2 h(v ) = 2gR - v2 where R = 6.4 x 10' m is the radius of the earth and g = 9.8m/s' is the acceleration due to gravity. Use a graphing device to draw a graph of the function h. (Note that h and v must both be positive, so the viewing rectangle need not contain negative values.) What does the vertical asymptote represent physically? Here is a tip: At the vertical asymptote, the denominator of the rational function vanishes. Explanation Graph the function P(v): Use a for v and graph y = P(x) in the graphing utility. Set the window size to 0. 400 by 0. 5000 Note that the graph of P(x) = Po SO SO must have a vertical asymptote at values of a that satisfy 50 - = 0. 332 4 = 0 332 - T . Thus, the function must have a horizontal asymptote at z = 332 4500