A ballet dancer jumps in the air. The height, h(t), in feet, of the dancer at time t, in

Chapter 3, Problem 3.2.31

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A ballet dancer jumps in the air. The height, h(t), in feet, of the dancer at time t, in seconds since the start of the jump, is given by4 h(t) = 16t 2 + 16T t, where T is the total time in seconds that the ballet dancer is in the air. (a) Why does this model apply only for 0 t T? (b) When, in terms of T, does the maximum height of the jump occur? (c) Show that the time, T, that the dancer is in the air is related to H, the maximum height of the jump, by the equation H = 4T 2 .

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