Show that the path traced by the model rocket in Example 3 is a parabola by eliminating the parameter.

EXAMPLE 3 A model rocket follows the trajectory c(t) = (80t, 200t - 4.91) until it hits the ground, with t in seconds and distance in meters (Figure 4). Find: (a) The rocket's height at t = 5 s. (b) Its maximum height. y (m) 2000 1000 1=0 1=5 t=20.4 1,000 2,000 1=40.8 3,000 - x (m)