Question

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. height of penny over time

t	h(t)
0.1	1.951
0.2	1.804
0.3	1.559
0.4	1.216
0.5	0.775
0.6	0.236
0.7	-0.401
0.8	-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

Explanation:

Step1: Identify ground - hitting condition

The penny hits the ground when $h(t)=0$. We look at the values in the table.

Step2: Analyze table values

When $t = 0.6$, $h(t)=0.236$ and when $t = 0.7$, $h(t)=- 0.401$. The height changes sign between $t = 0.6$ and $t = 0.7$. Since we want the time when it hits the ground (height $h(t)$ crosses from positive to negative), and we are asked for the value to the nearest tenth of a second, the time is $0.7$ seconds.

Answer:

0.7 seconds