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Since \( a < 0 \), the parabola opens downward, so the maximum occurs at the vertex: \( t = -\frac{b}{2a} = -\frac{150}{2(-5)} = 15 \) seconds.
Now substitute \( t = 15 \) into \( h(t) \):
\( h(15) = -5(15)^2 + 150(15) + 100 = -5(225) + 2250 + 100 = -1125 + 2250 + 100 = 1225 \) meters.

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