Question

when hiking Marek throws a rock off a cliff that is roughly 10 meters above a lake. this situation is modeled by the equation h = -4.9t^2 + 10 with h representing the height in meters and t the time in seconds. if you were to set up a table to determine when the rock hits the water what would be a reasonable scale for the range?

Answer 1

First find when it hits the water: set h = 0.

0 = −4.9t^2 + 10 → t^2 = 10/4.9 → t ≈ 1.43 s.

So the outputs (range) run from the initial height 10 m down to 0 m. A reasonable scale for the range is 0 to 10 meters (tick marks every 1 or 2 m). For the domain use t from 0 to about 1.5 s (tick marks every 0.1–0.25 s).

Example table (t in s, h in m):

- t = 0.00 → h = 10.00
- t = 0.25 → h ≈ 9.69
- t = 0.50 → h ≈ 8.78
- t = 0.75 → h ≈ 7.24
- t = 1.00 → h = 5.10
- t = 1.25 → h ≈ 2.34
- t ≈ 1.43 → h = 0 (impact)