Lara made the table below of the predicted values for h(t), the height, in meters, of a penny t seconds after it is dropped off of the back of the bleachers.

Question

A 2-column table with 9 rows titled Height of Penny over Time. The first column is labeled t with entries 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8. The second column is labeled h(t) with entries 2, 1.951, 1.804, 1.559, 1.216, 0.775, 0.236, negative 0.401, negative 1.136.
To the nearest tenth of a second, how much time would it take the penny to hit the ground?

0.5 seconds
0.6 seconds
0.7 seconds
0.8 seconds

Answer 1

To determine when the penny hits the ground, we need to find when the height \( h(t) \) becomes zero or negative.

From the table:

• At \( t = 0.5 \) seconds, \( h(0.5) = 0.775 \) meters (above ground).
• At \( t = 0.6 \) seconds, \( h(0.6) = 0.236 \) meters (still above ground).
• At \( t = 0.7 \) seconds, \( h(0.7) = -0.401 \) meters (below ground, indicating it has hit the ground).
• At \( t = 0.8 \) seconds, \( h(0.8) = -1.136 \) meters (still below ground).

Since the penny is still above ground at \( t = 0.6 \) and has hit the ground by \( t = 0.7 \) seconds, we conclude that it takes approximately 0.7 seconds for the penny to hit the ground.

Thus, the answer is 0.7 seconds.