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5-81.

Evaluate v(t) when t = 0.

Evaluate h(t) when t = 0.

Since the height function is a parabola, the maximum height can be determined by using Algebra to locate the vertex. Calculus can also be used.

The maximum height will occur at the time when v(t) = 0.

The vertex of the parabola is located at t = –21/2(–4.9) ≈ 2.143 seconds.
h(2.143) ≈ 25.5 m