Question

Airplane height, in feet: h = 144
Baseball height, in feet: h = 96t – 16t2
Choose the graph of the system shown above.

Answer 1

The parabola h = 96t − 16t^2 opens downward with vertex at t = 96/(2·16) = 3 and h(3) = 96·3 − 16·9 = 144, so its maximum point is (3, 144). The horizontal line is h = 144. Solving 96t − 16t^2 = 144 gives (t − 3)^2 = 0, so the parabola is tangent to the line at (3,144).

So choose the graph that shows:
- a horizontal line at h = 144, and
- a downward-opening parabola whose vertex touches that line at (3,144) (and which crosses the t-axis at t = 0 and t = 6).