Question

A ball is dropped from above ground level and hits the ground sometime between 4 and 6 seconds after it is dropped. The ball's height in meters is modeled by a function h(t), where t represents time in seconds. Which table most likely relates to this function?

A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 70, 50.4, negative 8.4, negative 106.4.

A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 100, 80.4, 21.6, negative 76.4.

A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries negative 150, negative 130.4, negative 71.6, 26.4.

A 2-column table with 4 rows. The first column is labeled t with entries 0, 2, 4, 6. The second column is labeled h(t) with entries 180, 160.4, 101.6, 3.6.

Answer 1

Table B.

Reason: for a drop from above ground you need h(0) > 0, h(4) > 0 and h(6) < 0 (so the height crosses zero between 4 and 6 s). Table B gives 100, 80.4, 21.6, −76.4, which fits (and matches h(t) = 100 − 4.9t^2).